Last update:
Fri Mar 8 12:16:53 MST 2024
Steven A. Orszag Introductory statement . . . . . . . . . 1--2
Victor Yakhot and
Steven A. Orszag Renormalization group analysis of
turbulence. I. Basic theory . . . . . . 3--51
Daniel M. Nosenchuck and
Michael G. Littman Two-dimensional nonsteady viscous flow
simulation on the Navier--Stokes
Computer miniNode . . . . . . . . . . . 53--73
Steven A. Orszag and
Moshe Israeli and
Michel O. Deville Boundary conditions for incompressible
flows . . . . . . . . . . . . . . . . . 75--111
Anonymous Important announcement . . . . . . . . . 113--113
N. Metropolis Massively parallel processing . . . . . 115--116
G. B. McFadden and
P. W. Voorhees and
R. F. Boisvert A boundary integral method for the
simulation of two-dimensional particle
coarsening . . . . . . . . . . . . . . . 117--144
L. Hannon and
G. C. Lie and
E. Clementi Molecular dynamics simulation of flow
past a plate . . . . . . . . . . . . . . 145--150
William P. Dannevik Efficient solution of non-Markovian
covariance evolution equations in fluid
turbulence . . . . . . . . . . . . . . . 151--182
John P. Boyd An analytical and numerical study of the
two-dimensional Bratu equation . . . . . 183--206
Anonymous Important announcement . . . . . . . . . 1--1
Moshe Dubiner Asymptotic analysis of spectral methods 3--31
L. Goldhirsch and
Steven A. Orszag and
B. K. Maulik An efficient method for computing
leading eigenvalues and eigenvectors of
large asymmetric matrices . . . . . . . 33--58
R. Morison and
S. Otto The scattered decomposition for finite
elements . . . . . . . . . . . . . . . . 59--76
Mujeeb R. Malik and
Steven A. Orszag Linear stability analysis of
three-dimensional compressible boundary
layers . . . . . . . . . . . . . . . . . 77--97
John P. Boyd Exponentially convergent
Fourier--Chebshev quadrature schemes on
bounded and infinite intervals . . . . . 99--109
B. J. Bayly and
I. Goldhirsch and
Steven A. Orszag Independent degrees of freedom of
dynamical systems . . . . . . . . . . . 111--121
Bertil Gustafsson Unsymmetric hyperbolic systems and the
Euler equations at low Mach numbers . . 123--136
W. C. Thacker A cost-function approach to the
assimilation of asynoptic data . . . . . 137--158
J. H. Ong An algorithm for frontwidth reduction 159--173
Raad A. Fatoohi and
Chester E. Grosch Implementation of an ADI Method on
parallel computers . . . . . . . . . . . 175--193
F. Pasquarelli and
A. Quarteroni and
G. Sacchi-Landriani Spectral approximations of the Stokes
problem by divergence-free functions . . 195--226
J. Andrzej Domaradzki and
Steven A. Orszag Numerical solutions of the direct
interaction approximation equations for
anisotropic turbulence . . . . . . . . . 227--248
David A. Kopriva A practical assessment of spectral
accuracy for hyperbolic problems with
discontinuities . . . . . . . . . . . . 249--262
Edward T. Bullister and
Steven A. Orszag Numerical simulation of turbulent spots
in channel and boundary layer flows . . 263--281
Robert T. Smith and
Csaba K. Zoltani An application of the finite element
method to maximum entropy tomographic
image reconstruction . . . . . . . . . . 283--295
J. J. Derby and
L. J. Atherton and
P. D. Thomas and
R. A. Brown Finite-element methods for analysis of
the dynamics and control of Czochralski
crystal growth . . . . . . . . . . . . . 297--343
Y. Reuven and
M. D. Smooke and
H. Rabitz Sensitivity analysis of one-dimensional
mixed initial-boundary value problems:
Application to freely propagating
premixed laminar flames . . . . . . . . 345--370
S. I. Hariharan and
S. I. Sudharsanan Wave envelope technique for multimode
wave guide problems . . . . . . . . . . 371--387
Einar M. Rònquist and
Anthony T. Patera Spectral element multigrid. I.
Formulation and numerical results . . . 389--406
Luis G. Reyna $ L_2 $ estimates for Chebyshev
collocation . . . . . . . . . . . . . . 1--23
Andy D. Leonard and
James C. Hill Direct numerical simulation of turbulent
flows with chemical reaction . . . . . . 25--43
Alfio Quarteroni and
Giovanni Sacchi-Landriani Domain decomposition preconditioners for
the spectral collocation method . . . . 45--76
L. H. Ungar and
N. Ramprasad and
R. A. Brown Finite element methods for unsteady
solidification problems arising in
prediction of morphological structure 77--108
John P. Boyd Chebyshev domain truncation is inferior
to Fourier domain truncation for solving
problems on an infinite interval . . . . 109--120
C. H. Liu and
T. C. Wong and
O. A. Kandil Separation-bubble flow solution using
Euler/Navier--Stokes zonal approach with
downstream compatibility conditions . . 121--137
Victor Yakhot and
Steven A. Orszag and
Raj Panda Computational test of the
renormalization group theory of
turbulence . . . . . . . . . . . . . . . 139--147
Pieter G. Buning Sources of error in the graphical
analysis of CFD results . . . . . . . . 149--164
J. B. Greenberg Self-regulating finite-difference
methods for the computation of reacting
flows with nonlinear kinetics . . . . . 165--187
Tor O. Saetre and
Nils Ryum Dynamic simulation of grain boundary
migration . . . . . . . . . . . . . . . 189--199
Avram Sidi and
Moshe Israeli Quadrature methods for periodic singular
and weakly singular Fredholm integral
equations . . . . . . . . . . . . . . . 201--231
Antony Jameson Aerodynamic design via control theory 233--260
Shlomo Ta'asan Multigrid method for stability problems 261--274
Saul Abarbanel and
Ajay Kumar Compact high-order schemes for the Euler
equations . . . . . . . . . . . . . . . 275--288
Yi-ling F. Chiang and
Ji-Suing Ma and
Kuo-Lin Hu Parallel multischeme computation . . . . 289--306
Clement B. Somuah and
Syed M. Islam A class of multiple time scale
algorithms for simulating power system
frequency dynamics . . . . . . . . . . . 307--322
Yvon Maday and
Rafael Munoz Spectral element multigrid. II.
Theoretical justification . . . . . . . 323--353
K. N. Christodoulou and
L. E. Scriven Finding leading modes of a viscous free
surface flow: An asymmetric generalized
eigenproblem . . . . . . . . . . . . . . 355--406
Zhen-Su She and
Eric Jackson and
Steven A. Orszag Scale-dependent intermittency and
coherence in turbulence . . . . . . . . 407--434
W. W. Schultz and
N. Y. Lee and
J. P. Boyd Chebyshev pseudospectral method of
viscous flows with corner singularities 1--24
Hillel Tal-Ezer Polynomial approximation of functions of
matrices and applications . . . . . . . 25--60
Sauro Succi and
Maurizio Benassi A four-color parallel algorithm for the
solution of a two-dimensional
advection-diffusion equation with the
finite element method . . . . . . . . . 61--70
Nira Gruberger Spectral methods for the computation of
discontinuous solutions . . . . . . . . 71--117
Frederic Bisshopp Characteristic lines for two- and
three-dimensional flows . . . . . . . . 119--137
A. Yakhot and
S. A. Orszag and
V. Yakhot and
M. Israeli Renormalization group formulation of
large-eddy simulations . . . . . . . . . 139--158
Pelle Olsson and
S. Lennart Johnson Boundary modifications of the
dissipation operators for the
three-dimensional Euler equations . . . 159--195
Thomas A. Zang and
Steven E. Krist and
M. Yousuff Hussaini Resolution requirements for numerical
simulations of transition . . . . . . . 197--217
S. Balachandar and
M. R. Maxey and
L. Sirovich Numerical simulation of high Rayleigh
number convection . . . . . . . . . . . 219--236
Gregory R. Baker and
Daniel I. Meiron and
Steven A. Orszag Generalized vortex methods for free
surface flow problems. II: Radiating
waves . . . . . . . . . . . . . . . . . 237--259
Milton E. Rose Compact finite volume methods for the
diffusion equation . . . . . . . . . . . 261--290
A. G. Tomboulides and
M. Israeli and
G. E. Karniadakis Efficient removal of boundary-divergence
errors in time-splitting methods . . . . 291--308
David Gottlieb and
Richard S. Hirsh Parallel pseudospectral domain
decomposition techniques . . . . . . . . 309--325
Richard A. Friesner and
Laurette S. Tuckerman A method for exponential propagation of
large systems of stiff nonlinear
differential equations . . . . . . . . . 327--354
Nigel Goldenfeld and
Olivier Martin and
Y. Oono Intermediate asymptotics and
renormalization group theory . . . . . . 355--372
Shigeo Kida and
Steven A. Orszag Enstrophy budget in decaying
compressible turbulence . . . . . . . . 1--34
Yi-ling F. Chiang and
Jih-Fu Lai Parallel multischeme computation with
the switch of computation history . . . 35--53
U. Ehrenstein The spectrum of a Chebyshev--Fourier
approximation for the Stokes equations 55--84
Shigeo Kida and
Steven A. Orszag Energy and spectral dynamics in forced
compressible turbulence . . . . . . . . 85--125
Chi-Wang Shu Numerical experiments on the accuracy of
ENO and modified ENO schemes . . . . . . 127--149
A. M. Rogerson and
E. Meiburg A numerical study of the convergence
properties of ENO schemes . . . . . . . 151--167
Milton E. Rose An implicit enthalpy scheme for
one-phase Stefan problems . . . . . . . 169--185
J. R. Parker A system for fast erosion and dilation
of Bi-level images . . . . . . . . . . . 187--198
Victor Yakhot and
Steven A. Orszag and
S. Balachandar Phenomenological theory of probability
distributions in turbulence . . . . . . 199--221
D. Gottlieb and
C. L. Streett Quadrature imposition of compatibility
conditions in Chebyshev methods . . . . 223--239
Steven A. Orszag and
Victor Yakhot Inhibition of mixing and self-focusing
in high Mach number turbulence . . . . . 241--243
David C. O'Neal Optimization of finite element codes . . 245--262
Y. Maday and
Anthony T. Patera and
Einar M. Rònquist An Operator-integration-factor splitting
method for time-dependent problems:
Application to incompressible fluid flow 263--292
A. Dubey and
M. Zubair and
C. E. Grosch Computing the Fourier transform of real
data on a hypercube . . . . . . . . . . 293--309
John P. Boyd The envelope of the error for
trigonometric and Chebyshev
interpolation . . . . . . . . . . . . . 311--363
Wilhelm Heinrichs Stabilization techniques for spectral
methods . . . . . . . . . . . . . . . . 1--19
Andreas Karageorghis A note on the satisfaction of the
boundary conditions for Chebyshev
collocation methods in rectangular
domains . . . . . . . . . . . . . . . . 21--26
Eric Jackson and
Zhen-Su She and
Steven A. Orszag A case study in parallel computing: I.
Homogeneous turbulence on a hypercube 27--45
Peisen Zhang Simpson's rule of discretized Feynman
path integration . . . . . . . . . . . . 47--60
John H. Halton Random sequences in Fréchet spaces . . . 61--77
Anonymous Editorial statement . . . . . . . . . . I--II
Ron Henderson and
George Em. Karniadakis Hybrid spectral-element-low-order
methods for incompressible flows . . . . 79--100
B. Christer V. Johansson Well-posedness in the generalized sense
for the incompressible Navier--Stokes
equation . . . . . . . . . . . . . . . . 101--127
Seymour V. Parter and
Sze-Ping Wong Preconditioning second-order elliptic
operators: Condition numbers and the
distribution of the singular values . . 129--157
Hervé Vandeven Family of spectral filters for
discontinuous problems . . . . . . . . . 159--192
Grant O. Cook, Jr. and
Jeffrey F. Painter and
Stewart A. Brown How symbolic computation boosts
productivity in the simulation of
partial differential equations . . . . . 193--209
Alexander G. Cheremensky Robust frequency design of linear
stationary systems in aeroautoelastics 211--227
Eytan Barouch and
John W. Cahn and
Uwe Hollerbach Numerical simulation of submicron
photolithographic processing . . . . . . 229--250
D. J. Groh and
R. A. Marshall and
A. B. Kunz and
C. R. Givens An approximation method for eigenvectors
of very large matrices . . . . . . . . . 251--267
Charlie H. Cooke and
Tze-Jang Chen Continuous front tracking with subcell
resolution . . . . . . . . . . . . . . . 269--282
Yi-Ling F. Chiang Error approximation in the solution of a
linear PDE initial-valued problem . . . 283--303
Fabio Guerinoni An appropriate mesh representation for
tetrahedral finite volume computations 305--321
David L. Book and
Chiping Li and
Gopal Patnaik Quantifying residual numerical diffusion
in flux-corrected transport algorithms 323--343
Moshe Dubiner Spectral methods on triangles and other
domains . . . . . . . . . . . . . . . . 345--390
B. Christer V. Johansson Well-posedness in the generalized sense
for boundary layer suppressing boundary
conditions . . . . . . . . . . . . . . . 391--414
John H. Halton Random sequences in generalized Cantor
sets . . . . . . . . . . . . . . . . . . 415--423
S. Gama and
U. Frisch and
H. Scholl The two-dimensional Navier--Stokes
equations with a large-scale instability
of the Kuramoto--Sivashinsky type:
Numerical exploration on the Connection
Machine . . . . . . . . . . . . . . . . 425--452
José M. Carcione Domain decomposition for wave
propagation problems . . . . . . . . . . 453--472
Shigeo Kida and
Steven A. Orszag Energy and spectral dynamics in decaying
compressible turbulence . . . . . . . . 1--34
Victor Yakhot and
Leslie M. Smith The renormalization group, the $
\epsilon $-expansion and derivation of
turbulence models . . . . . . . . . . . 35--61
Yih Nen Jeng and
Yuan Chang Liou A new adaptive grid generation by
elliptic equations with orthogonality at
all of the boundaries . . . . . . . . . 63--80
Bahrom B. Sanugi An iterative multistep formula for
solving initial value problems . . . . . 81--94
Wilhelm Heinrichs A stabilized multidomain approach for
singular perturbation problems . . . . . 95--125
R. Bhogeswara and
J. E. Killough Domain decomposition and multigrid
solvers for flow simulation in porous
media on distributed memory parallel
processors . . . . . . . . . . . . . . . 127--162
Hans Babovsky Efficient treatment of collisions in
simulation codes for heavy-ion reactions 163--174
G. Dattoli and
C. Mari and
A. Torre and
C. Chiccoli Analytical and numerical results on
$M$-variable generalized Bessel
functions . . . . . . . . . . . . . . . 175--196
M. F. Berger Hierarchical gradient methods for
nonlinear LSQ problems . . . . . . . . . 197--228
Alexander Yakhot and
Omer Kedar and
Steven A. Orszag An algebraic-Q4 turbulent eddy viscosity
model: Boundary layer flow over a flat
plate and flow in a pipe . . . . . . . . 229--239
M. H. Whang and
S. P. Kuo and
M. C. Lee Numerical analysis of coupled
hydromagnetic wave equations with a
finite difference scheme . . . . . . . . 241--261
S. N. Gupta and
M. Zubair and
C. E. Grosch A multigrid algorithm for parallel
computers: CPMG . . . . . . . . . . . . 263--279
John H. Halton Reject the rejection technique . . . . . 281--287
Hong Yang and
J. Michael Orszag Numerical computation of $ H^\infty $
optimal performance . . . . . . . . . . 289--311
Kelly Black Polynomial collocation using a domain
decomposition solution to parabolic
PDE's via the penalty method and
explicit/implicit time marching . . . . 313--338
Yih Nen Jeng and
Uon Jien Payne The application of the locally implicit
method to upwind TVD schemes . . . . . . 339--357
Rafhat Iqbal A one-pass algorithm for
shape-preserving quadratic spline
interpolation . . . . . . . . . . . . . 359--376
I. Goldhirsch and
M.-L. Tan and
G. Zanetti A molecular dynamical study of granular
fluids I: The unforced granular gas in
two dimensions . . . . . . . . . . . . . 1--40
V. A. Zheligovsky Numerical solution of the kinematic
dynamo problem for Beltrami flows in a
sphere . . . . . . . . . . . . . . . . . 41--68
G. Dattoli and
C. Chiccoli and
S. Lorenzutta and
G. Maino Advances on the theory of generalized
Bessel functions and applications to
multiphoton processes . . . . . . . . . 69--109
Alexander Yakhot and
Steven A. Orszag Numerical simulation of turbulent flow
in the inlet region of a smooth pipe . . 111--121
Andreas Karageorghis Conforming Chebyshev spectral methods
for Poisson problems in rectangular
domains . . . . . . . . . . . . . . . . 123--133
M. Israeli and
L. Vozovoi and
A. Averbuch Spectral multidomain technique with
Local Fourier Basis . . . . . . . . . . 135--149
M. Israeli and
L. Vozovoi and
A. Averbuch Parallelizing implicit algorithms for
time-dependent problems by parabolic
domain decomposition . . . . . . . . . . 151--166
T. Dubois and
F. Jauberteau and
R. Temam Solution of the incompressible
Navier--Stokes equations by the
nonlinear Galerkin method . . . . . . . 167--194
Ludmila Ioffe and
Shlomit S. Pinter Applying asynchronous parallel
characteristic methods for solving
systems of hyperbolic PDEs . . . . . . . 195--218
S. Succi and
D. d'Humi\`eres and
Y. H. Qian and
S. A. Orszag On the small-scale dynamical behavior of
lattice BGK and lattice Boltzmann
schemes . . . . . . . . . . . . . . . . 219--230
Y. H. Qian Simulating thermohydrodynamics with
lattice BGK models . . . . . . . . . . . 231--242
J. R. Parker and
G. Groisman Simulated annealing for data modeling in
scientific images . . . . . . . . . . . 243--266
Leland Jameson On the wavelet based differentiation
matrix . . . . . . . . . . . . . . . . . 267--305
B. Christer and
V. Johansson The use of Richardson extrapolation for
the numerical solution of low Mach
number flow in confined regions . . . . 307--340
C. Liu and
Z. Liu and
S. McCormick Multilevel adaptive methods for laminar
diffusion flames . . . . . . . . . . . . 341--355
Hoa D. Nguyen and
Seungho Paik A noniterative solution approach for
parallel pseudospectral domain
decomposition . . . . . . . . . . . . . 357--372
M. Reza Mehrabi and
Robert A. Brown An incomplete nested dissection
algorithm for parallel direct solution
of finite element discretizations of
partial differential equations . . . . . 373--387
Wilhelm Heinrichs Distributive relaxations for the
spectral Stokes operator . . . . . . . . 389--398
D. Boffi and
D. Funaro An alternative approach to the analysis
and the approximation of the
Navier--Stokes equations . . . . . . . . 1--16
Alexander G. Cheremensky Principle of feedback with additive
system disturbances and some compensator
schemes . . . . . . . . . . . . . . . . 17--37
Ivar Lie Multidomain solution of advection
problems by Chebyshev spectral
collocation . . . . . . . . . . . . . . 39--64
Shun-Shii Lin A chained-matrices approach for parallel
computation of continued fractions and
its applications . . . . . . . . . . . . 65--80
John P. Boyd Hyperviscous shock layers and diffusion
zones: Monotonicity, spectral viscosity,
and pseudospectral methods for very high
order differential equations . . . . . . 81--106
W. Couzy and
M. O. Deville Spectral-element preconditioners for the
Uzawa pressure operator applied to
incompressible flows . . . . . . . . . . 107--122
Yong Luo and
Matthew J. Yedlin Polynomial time-marching for nonperiodic
boundary value problems . . . . . . . . 123--136
Wilhelm Heinrichs Spectral viscosity for convection
dominated flow . . . . . . . . . . . . . 137--148
Zi-Cai Li Advanced splitting-integrating methods
with high convergence rates for
restoring images and patterns . . . . . 149--172
H. Schaeben Analogy and duality of texture analysis
by harmonics or indicators . . . . . . . 173--195
Rafhat Iqbal An algorithm for convexity-preserving
surface interpolation . . . . . . . . . 197--212
John H. Halton Sequential Monte Carlo techniques for
the solution of linear systems . . . . . 213--257
A. Noullez and
M. Vergassola A fast Legendre transform algorithm and
applications to the adhesion model . . . 259--281
A. Yakhot and
S. Rakib and
W. S. Flannery Low-Reynolds number approximation for
turbulent eddy viscosity . . . . . . . . 283--292
P. Falsaperla and
S. Motta and
S. Succi Parallel efficiency of the C.R.F. method
on an IBM RS/6000 cluster platform . . . 293--309
L. Vozovoi and
M. Israeli and
A. Averbuch Spectral multidomain technique with
Local Fourier Basis II: Decomposition
into cells . . . . . . . . . . . . . . . 311--326
Charlie H. Cooke and
Sang Kyu Yang Multi-resolution analysis with frontal
decomposition . . . . . . . . . . . . . 327--340
Andreas Karageorghis Conforming spectral methods for Poisson
problems in cuboidal domains . . . . . . 341--350
Hoa D. Nguyen and
Seungho Paik Solution domain decomposition method for
viscous incompressible flow . . . . . . 351--368
Charles G. Speziale and
Ridha Abid and
Paul A. Durbin On the realizability of Reynolds stress
turbulence closures . . . . . . . . . . 369--403
Martine Marion On the stability of collocation methods
for the two-dimensional Burgers
equation- The Fourier case . . . . . . . 405--417
E. Zampieri On the condition number of some spectral
collocation operators and their finite
element preconditioning . . . . . . . . 419--443
Pelle Olsson The numerical behavior of high-order
finite difference methods . . . . . . . 445--466
Alain Sei and
William Symes Dispersion analysis of numerical wave
propagation and its computational
consequences . . . . . . . . . . . . . . 1--27
Alex Solomonoff Reconstruction of a discontinuous
function from a few Fourier coefficients
using Bayesian estimation . . . . . . . 29--80
Jean-Pierre Croisille and
Rabia Khanfir and
Gérard Chanteur Numerical simulation of the MHD
equations by a kinetic-type method . . . 81--92
M. Reza Mehrabi and
Robert A. Brown Parallel implementation of
finite-element/Newton method for
solution of steady-state and transient
nonlinear partial differential equations 93--137
C. Trayner and
M. H. Glowacki A new technique for the solution of the
Saha equation . . . . . . . . . . . . . 139--149
R. S. Miller and
F. A. Jaberi and
C. K. Madnia and
P. Givi The structure and the small-scale
intermittency of passive scalars in
homogeneous turbulence . . . . . . . . . 151--180
U. Schumann and
M. Strietzel Parallel solution of tridiagonal systems
for the Poisson equation . . . . . . . . 181--190
Alexander B. Konstantinov and
Steven A. Orszag Extended Lagrangian particle-in-cell
(ELPIC) code for inhomogeneous
compressible flows . . . . . . . . . . . 191--231
Ronald D. Joslin and
Ulf R. Hanebutte and
Mohammad Zubair Scalability of parallel spatial direct
numerical simulations on Intel Hypercube
and IBM SP1 and SP2 . . . . . . . . . . 233--269
Iwao Hosokawa and
Kiyoshi Yamamoto Conditional Fourier spectral method for
direct numerical simulation of
incompressible flows . . . . . . . . . . 271--287
F. Pasquarelli Spectral multidomain approximation of
elliptic problems with mixed conditions
on the interfaces . . . . . . . . . . . 289--304
José Gómez-Valdés and
Dong-Ping Wang Massively parallel processing in coastal
ocean circulation model . . . . . . . . 305--323
James F. Geer Rational trigonometric approximations
using Fourier series partial sums . . . 325--356
Chi-Wang Shu and
Peter S. Wong A note on the accuracy of spectral
method applied to nonlinear conservation
laws . . . . . . . . . . . . . . . . . . 357--369
Lucia Dettori and
David Gottlieb and
Roger Temam A nonlinear Galerkin method: The
two-level Fourier-collocation case . . . 371--389
Sang Kyu Yang and
Charlie H. Cooke Multi-resolution analysis on the
interval with natural spline projection
and uniform two-scale relation . . . . . 391--407
Nikolai N. Kukharkin Coherent structure formation, phase
correlations, and finite-size effects in
$2$D turbulence . . . . . . . . . . . . 409--448
Valipuram S. Manoranjan and
Yafang Song A simple ILU preconditioning coupled to
Orthomin method . . . . . . . . . . . . 1--12
Semion Sukoriansky and
Alexei Chekhlov and
Steven A. Orszag Large eddy simulation of two-dimensional
isotropic turbulence . . . . . . . . . . 13--45
Irad Yavneh and
James C. McWilliams Multigrid solution of stably stratified
flows: The quasigeostrophic equations 47--69
A. Yakhot and
E. Shalman and
O. Igra and
Y. Yadlin An algebraic-$ Q_4 $ turbulence model
for attached and separated airfoil flows 71--98
Chang-Ock Lee A comparison of some standard elliptic
solvers: CM-5 vs. Cray C-90 . . . . . . 99--126
Abdul J. Jerri and
Russell L. Herman The solution of the Poisson--Boltzmann
equation between two spheres: Modified
iterative method . . . . . . . . . . . . 127--153
Jyh-Jia Chen and
Chyi Hwang Characterization of robust root loci of
polytopes of polynomials . . . . . . . . 155--166
A. Karageorghis and
N. S. Stylianopoulos and
H. A. Zachariades A numerical conformal mapping method for
harmonic mixed boundary value problems 167--178
F. Ladeinde and
E. E. O'Brien and
X. D. Cai A parallelized ENO procedure for direct
numerical simulation of compressible
turbulence . . . . . . . . . . . . . . . 179--205
Josef Stricker and
Yair Censor and
Boris Zakharin Inhomogeneous turbulent field
diagnostics by distance-dependent
tomographic reconstruction techniques 207--227
Bertil Gustafsson and
Pelle Olsson High-order centered difference methods
with sharp shock resolution . . . . . . 229--260
Anonymous Important announcement . . . . . . . . . 297--297
M. C. Ciccoli Adaptive domain decomposition algorithms
and finite volume/finite element
approximation for advection-diffusion
equations . . . . . . . . . . . . . . . 299--341
John C. Bowman A wavenumber partitioning scheme for
two-dimensional statistical closures . . 343--372
Wei-Ming Cao and
Claudio Carlenzoli A projection method for long-term
computation of Navier--Stokes equations 373--395
Wilhelm Heinrichs High-order time splitting for the Stokes
equations . . . . . . . . . . . . . . . 397--410
W. B. Liu and
Jie Shen A new efficient spectral Galerkin method
for singular perturbation problems . . . 411--437
Uwe Hollerbach Effects of Aliasing Errors on
Microlithographic Image Computations . . 3--10
Erik Brakkee and
Peter Wilders The Influence of Interface Conditions on
Convergence of Krylov--Schwarz Domain
Decomposition for the
Advection--Diffusion Equation . . . . . 11--30
Yong Luo and
Matthew J. Yedlin Polynomial Time-Marching for
Nonreflecting Boundary Problems . . . . 31--50
Y. C. Hon and
X. Z. Mao A Multiquadric Interpolation Method for
Solving Initial Value Problems . . . . . 51--55
Glenn R. Ierley A Class of Sparse Spectral Operators for
Inversion of Powers of the Laplacian in
$N$ Dimensions . . . . . . . . . . . . . 57--73
Hoa D. Nguyen and
Seungho Paik and
Rod W. Douglass A Legendre--Spectral Element Method for
Flow and Heat Transfer About an
Accelerating Droplet . . . . . . . . . . 75--97
Daoqi Yang A Parallel Grid Modification and Domain
Decomposition Algorithm for Local
Phenomena Capturing and Load Balancing 99--117
Knut S. Eckhoff On a High Order Numerical Method for
Solving Partial Differential Equations
in Complex Geometries . . . . . . . . . 119--138
A. G. Tomboulides and
J. C. Y. Lee and
S. A. Orszag Numerical Simulation of Low Mach Number
Reactive Flows . . . . . . . . . . . . . 139--167
Y. Chen and
H. Ohashi and
M. Akiyama Two-Parameter Thermal Lattice BGK Model
with a Controllable Prandtl Number . . . 169--185
Seyoung Oh and
Seungho Paik and
Hoa D. Nguyen Solution-Domain-Decomposition Method for
Heat Transfer Problem Using Parallel
Distributed Computing . . . . . . . . . 187--204
Cristina Cunha and
Sônia M. Gomes A Shock Indicator for Adaptive Schemes
for Conservation Laws . . . . . . . . . 205--214
P. J. van der Houwen and
B. P. Sommeijer Splitting Methods for Three-Dimensional
Transport Models with Interaction Terms 215--231
Nathalie Marco and
Bruno Koobus and
Alain Dervieux An Additive Multilevel Optimization
Method and Its Application to
Unstructured Meshes . . . . . . . . . . 233--251
James Geer and
Nana Saheb Banerjee Exponentially Accurate Approximations to
Piece-Wise Smooth Periodic Functions . . 253--287
H. Arsham Affine Geometric Method For Linear
Programs . . . . . . . . . . . . . . . . 289--303
Vadim Borue and
Steven A. Orszag Turbulent Convection Driven by a
Constant Temperature Gradient . . . . . 305--351
Weizhong Dai A Generalized Peaceman--Rachford ADI
Scheme for Solving Two-Dimensional
Parabolic Differential Equations . . . . 353--360
Weizhong Dai A New ADI Scheme for Solving
Three-Dimensional Parabolic Differential
Equations . . . . . . . . . . . . . . . 361--369
S. O. Kastner Symbolic Evaluation of Total Transition
Probabilities in Kinetic Systems:
Potential Applications . . . . . . . . . 371--384
Daniele Funaro Improving the Performances of Implicit
Schemes for Hyperbolic Equations . . . . 385--394
S. Succi and
G. Bella and
F. Papetti Lattice Kinetic Theory for Numerical
Combustion . . . . . . . . . . . . . . . 395--408
Jung-Gen Wu and
Wen-Ming Yan and
Kuo-Liang Chung A Parallel Solver for Circulant Toeplitz
Tridiagonal Systems on Hypercubes . . . 409--431
V. A. Zheligovsky and
O. M. Podvigina An Optimized Iterative Method for
Numerical Solution of Large Systems of
Equations Based on the Extremal Property
of Zeroes of Chebyshev Polynomials . . . 433--464
Yong Luo Polynomial Time-Marching for
Three-Dimensional Wave Equations . . . . 465--477
C. Birkeland and
R. Holmestad and
K. Marthinsen and
R. Hòier Use of Supercomputers in Quantitative
Electron Diffraction . . . . . . . . . . 1--18
Mats Holmström and
Johan Waldén Adaptive Wavelet Methods for Hyperbolic
PDEs . . . . . . . . . . . . . . . . . . 19--49
T. E. Simos Some Modified Runge--Kutta Methods for
the Numerical Solution of Initial-Value
Problems with Oscillating Solutions . . 51--63
R. Janardhan and
T. Downar A Nested FGMRES Method for Parallel
Calculation of Nuclear Reactor
Transients . . . . . . . . . . . . . . . 65--93
D. Funaro and
M. Giangi and
D. Mansutti A Splitting Method for Unsteady
Incompressible Viscous Fluids Imposing
No Boundary Conditions on Pressure . . . 95--104
Yuan Chang Liou and
Yih Nen Jeng A Transfinite Interpolation Method of
Grid Generation Based on Multipoints . . 105--114
Gabriella Puppo Bubble Stabilization of Spectral
Methods: The Multidimensional Case . . . 115--149
E. Shalman and
A. Yakhot and
S. Shalman and
O. Igra and
Y. Yadlin Attenuating Artificial Dissipation in
the Computation of Navier--Stokes
Turbulent Boundary Layers . . . . . . . 151--172
Sigal Gottlieb and
Paul F. Fischer Modified Conjugate Gradient Method for
the Solution of $ A x = b $ . . . . . . 173--183
Jerry L. Bickham and
Germana Peggion and
Benjamin R. Seyfarth Testing Moderately Parallel Environments
for an Ocean Modeling Application . . . 185--200
F. A. Jaberi and
C. K. Madnia Effects of Heat of Reaction on
Homogeneous Compressible Turbulence . . 201--228
Alexandre Konstantinov and
Ilya Staroselsky Renormalization Group-Based Transport
Modeling of Premixed Turbulent
Combustion: I. Incompressible
Deflagration Model . . . . . . . . . . . 229--252
Charles G. Speziale A Combined Large-Eddy Simulation and
Time-Dependent RANS Capability for
High-Speed Compressible Flows . . . . . 253--274
Paul Castillo and
Yousef Saad Preconditioning the Matrix Exponential
Operator with Applications . . . . . . . 275--302
H.-C. Chang and
D. Gottlieb and
M. Marion and
B. W. Sheldon Mathematical Analysis and Optimization
of Infiltration Processes . . . . . . . 303--321
T. Dubois and
F. Jauberteau A Dynamic Multilevel Model for the
Simulation of the Small Structures in
Homogeneous Isotropic Turbulence . . . . 323--367
Alexandr Konstantinov and
Steven A. Orszag Renormalization Group-Based Transport
Modeling of Premixed Turbulent
Combustion. II. Finite Density Gradient
and Direct Heat Release . . . . . . . . 369--404
Chung-Chiang Chou and
Yuefan Deng Numerical Solutions of a Nonlinear
Evolution System with Small Dissipation
on Parallel Processors . . . . . . . . . 405--417
Nana S. Banerjee and
James F. Geer Exponentially Accurate Approximations to
Periodic Lipschitz Functions Based on
Fourier Series Partial Sums . . . . . . 419--460
Yuehong Qian and
Jose Jimenez Note on a Fourth Order Finite Difference
Scheme for the Wave Equation . . . . . . 461--469
Yansi Zhang and
Steven A. Orszag Two-Equation RNG Transport Modeling of
High Reynolds Number Pipe Flow . . . . . 471--483
Jeng-Fan Leu and
Jyh-Cheng Jang and
Chyi Hwang Computation of Battle--Lemarie Wavelets
Using an FFT--Based Algorithm . . . . . 485--504
Yves Dubois-Pelerin and
Vincent van Kemenade An Object-Oriented Toolbox for Spectral
Element Analysis . . . . . . . . . . . . 1--29
F. A. Jaberi and
S. James Effects of Chemical Reaction on
Two-Dimensional Turbulence . . . . . . . 31--72
Wei Cai High-Order Mixed Current Basis Functions
for Electromagnetic Scattering of Curved
Surfaces . . . . . . . . . . . . . . . . 73--105
Andreas Karageorghis and
Marcin Paprzycki Conditioning of Pseudospectral Matrices
for Certain Domain Decompositions . . . 107--119
Michael S. Yeung Incident Wave Source for
Finite-Difference Time-Domain
Computation of Electromagnetic
Scattering for Objects Embedded in
Layered Dispersive Media . . . . . . . . 121--145
Steven A. Orszag and
Victor Yakhot Analysis of the $ \epsilon $-Expansion
in Turbulence Theory: Approximate
Renormalization Group for Diffusion of a
Passive Scalar in a Random Velocity
Field . . . . . . . . . . . . . . . . . 147--178
M. Giangi and
D. Mansutti and
G. Richelli Steady $3$D Flow Configurations for the
Horizontal Thermal Convection with
Thermocapillary Effects . . . . . . . . 179--195
Han Guoqiang and
Wang Jiong Extrapolation of Nyström Solution for
Two-Dimensional Nonlinear Fredholm
Integral Equations . . . . . . . . . . . 197--209
M. Bernaschi and
S. Succi and
G. Bella and
H. Chen Digital Physics Simulations of Reactive
Flow in a Catalytic Converter . . . . . 211--222
Bertil Gustafsson and
Lina Hemmingsson-Frändén A Fast Domain Decomposition High Order
Poisson Solver . . . . . . . . . . . . . 223--243
Huan-Chao Keh and
Jen-Chih Lin Simulation of Complete Binary Tree
Structures in a Faulty Flexible
Hypercube . . . . . . . . . . . . . . . 245--258
Frank G. Lether Thiele Rational Interpolation for the
Numerical Computation of the Reversible
Randles--Sevcik Function in
Electrochemistry . . . . . . . . . . . . 259--274
Wilhelm Heinrichs Spectral Approximation of Third-Order
Problems . . . . . . . . . . . . . . . . 275--289
Z. L. Guo and
B. C. Shi and
N. C. Wang Fully Lagrangian and Lattice Boltzmann
Methods for the Advection--Diffusion
Equation . . . . . . . . . . . . . . . . 291--300
George Kvernadze and
Thomas Hagstrom and
Henry Shapiro Locating Discontinuities of a Bounded
Function by the Partial Sums of Its
Fourier Series . . . . . . . . . . . . . 301--327
Kishor Ganguly and
Steven A. Orszag A New Time-Based Iterative Solver for
Linear Standing-Wave Problems . . . . . 329--346
Seymour V. Parter On the Legendre--Gauss--Lobatto Points
and Weights . . . . . . . . . . . . . . 347--355
Henrik Brandén and
Sverker Holmgren Convergence Acceleration for Hyperbolic
Systems Using Semicirculant
Approximations . . . . . . . . . . . . . 357--393
Michael S. Yeung Solution of Electromagnetic Scattering
Problems Involving Three-Dimensional
Homogeneous Dielectric Objects by the
Single Integral Equation Method . . . . 1--17
Hua-Zhong Tang and
Kun Xu Positivity-Preserving Analysis of
Explicit and Implicit Lax--Friedrichs
Schemes for Compressible Euler Equations 19--28
Bertil Gustafsson and
Jonas Nilsson Boundary Conditions and Estimates for
the Steady Stokes Equations on Staggered
Grids . . . . . . . . . . . . . . . . . 29--59
Fredrik Edelvik and
Gunnar Ledfelt Explicit Hybrid Time Domain Solver for
the Maxwell Equations in $3$D . . . . . 61--78
Saul Abarbanel and
Adi Ditkowski and
Bertil Gustafsson On Error Bounds of Finite Difference
Approximations to Partial Differential
Equations --- Temporal Behavior and Rate
of Convergence . . . . . . . . . . . . . 79--116
Ben-Yu Guo and
Jie Shen and
Zhong-Qing Wang A Rational Approximation and Its
Applications to Differential Equations
on the Half Line . . . . . . . . . . . . 117--147
D. Stanescu and
D. A. Kopriva and
M. Y. Hussaini Dispersion Analysis for Discontinuous
Spectral Element Methods . . . . . . . . 149--171
Tao Tang and
Jinghua Wang Convergence of MUSCL Relaxing Schemes to
the Relaxed Schemes for Conservation
Laws with Stiff Source Terms . . . . . . 173--195
Steeve Augoula and
Rémi Abgrall High Order Numerical Discretization for
Hamilton--Jacobi Equations on Triangular
Meshes . . . . . . . . . . . . . . . . . 197--229
Huanan Yang A Local Extrapolation Method for
Hyperbolic Conservation Laws. I. The ENO
Underlying Schemes . . . . . . . . . . . 231--264
Huaxiong Huang and
Brian R. Seymour Finite Difference Solutions of
Incompressible Flow Problems with Corner
Singularities . . . . . . . . . . . . . 265--292
Anne Gelb A Hybrid Approach to Spectral
Reconstruction of Piecewise Smooth
Functions . . . . . . . . . . . . . . . 293--322
Myungjoo Kang and
Ronald P. Fedkiw and
Xu-Dong Liu A Boundary Condition Capturing Method
for Multiphase Incompressible Flow . . . 323--360
Wenbin Liu and
Ningning Yan A Posteriori Error Estimators for a
Class of Variational Inequalities . . . 361--393
A. Chalabi and
Y. Qiu Relaxation Schemes for Hyperbolic
Conservation Laws with Stiff Source
Terms: Application to Reacting Euler
Equations . . . . . . . . . . . . . . . 395--416
Leland Jameson High Order Schemes for Resolving Waves:
Number of Points per Wavelength . . . . 417--439
Paul F. Fischer and
Sigal Gottlieb Solving $ A \underline x = \underline b
$ Using a Modified Conjugate Gradient
Method Based on Roots of $A$ . . . . . . 441--456
S. S. Ravindran Reduced-Order Adaptive Controllers for
Fluid Flows Using POD . . . . . . . . . 457--478
Frank G. Lether Analytical Expansion and Numerical
Approximation of the Fermi--Dirac
Integrals $ F_j(x) $ of Order $ j = - 1
/ 2 $ and $ j = 1 / 2 $ . . . . . . . . 479--497
S. J. Thomas and
R. D. Loft Parallel Semi-Implicit Spectral Element
Methods for Atmospheric General
Circulation Models . . . . . . . . . . . 499--518
Bengt Eliasson Outflow Boundary Conditions for the
Fourier Transformed One-Dimensional
Vlasov--Poisson System . . . . . . . . . 1--28
Ming Li and
Tao Tang A Compact Fourth-Order Finite Difference
Scheme for Unsteady Viscous
Incompressible Flows . . . . . . . . . . 29--45
I. Fatkullin and
J. S. Hesthaven Adaptive High-Order Finite-Difference
Method for Nonlinear Wave Problems . . . 47--67
F. G. Lether Variable Precision Algorithm for the
Numerical Computation of the
Fermi--Dirac Function $ F_j(x) $ of
Order $ j = - 3 / 2 $ . . . . . . . . . 69--79
Kelly Black and
John B. Geddes Spectral Hermite Approximations for the
Actively Mode-Locked Laser . . . . . . . 81--120
Qing Li and
Chu-Guang Zheng and
Neng-Chao Wang and
Bao-Chang Shi LBGK Simulations of Turing Patterns in
CIMA Model . . . . . . . . . . . . . . . 121--134
M. Bernaschi and
S. Succi and
H. Chen Accelerated Lattice Boltzmann Schemes
for Steady-State Flow Simulations . . . 135--144
Tie Zhou and
Yinfan Li and
Chi-Wang Shu Numerical Comparison of WENO Finite
Volume and Runge--Kutta Discontinuous
Galerkin Methods . . . . . . . . . . . . 145--171
Bernardo Cockburn and
Chi-Wang Shu Runge--Kutta Discontinuous Galerkin
Methods for Convection-Dominated
Problems . . . . . . . . . . . . . . . . 173--261
Houde Han and
Xin Wen The Local Artificial Boundary Conditions
for Numerical Simulations of the Flow
Around a Submerged Body . . . . . . . . 263--286
L. S. Hou Error Estimates for Semidiscrete Finite
Element Approximations of the Stokes
Equations Under Minimal Regularity
Assumptions . . . . . . . . . . . . . . 287--317
Bertrand Maury A Fat Boundary Method for the Poisson
Problem in a Domain with Holes . . . . . 319--339
Yiorgos-Sokratis Smyrlis and
Andreas Karageorghis Some Aspects of the Method of
Fundamental Solutions for Certain
Harmonic Problems . . . . . . . . . . . 341--371
Uwe Hollerbach and
Duan-Pin Chen and
Robert S. Eisenberg Two- and Three-Dimensional
Poisson--Nernst--Planck Simulations of
Current Flow Through Gramicidin A . . . 373--409
Ilaria Perugia and
Dominik Schötzau On the Coupling of Local Discontinuous
Galerkin and Conforming Finite Element
Methods . . . . . . . . . . . . . . . . 411--433
Wenbin Liu and
Ningning Yan Some a Posteriori Error Estimators for
$p$-Laplacian Based on Residual
Estimation or Gradient Recovery . . . . 435--477
Bruno Després and
Frédéric Lagouti\`ere Contact Discontinuity Capturing Schemes
for Linear Advection and Compressible
Gas Dynamics . . . . . . . . . . . . . . 479--524
Chris J. Budd and
Huaxiong Huang and
Robert D. Russell Mesh Selection for a Nearly Singular
Boundary Value Problem . . . . . . . . . 525--552
Abhinav Singh and
Yong Zhao Parallel Unstructured Dynamic Grid
Direct Monte Carlo Simulation of
Molecular Gas Dynamics and Its
Applications . . . . . . . . . . . . . . 553--568
Zhaoli Guo and
Chuguang Zheng and
T. S. Zhao A Lattice BGK Scheme with General
Propagation . . . . . . . . . . . . . . 569--585
Bertil Gustafsson Foreword . . . . . . . . . . . . . . . . 1--2
Paul Houston and
Max Jensen and
Endre Süli $ h p $-Discontinuous Galerkin Finite
Element Methods with Least-Squares
Stabilization . . . . . . . . . . . . . 3--25
Jue Yan and
Chi-Wang Shu Local Discontinuous Galerkin Methods for
Partial Differential Equations with
Higher Order Derivatives . . . . . . . . 27--47
Cem M. Albukrek and
Karsten Urban and
Dietmar Rempfer Divergence-Free Wavelet Analysis of
Turbulent Flows . . . . . . . . . . . . 49--66
Daniele Funaro Superconsistent Discretizations . . . . 67--79
Paul F. Fischer and
Gerald W. Kruse and
Francis Loth Spectral Element Methods for
Transitional Flows in Complex Geometries 81--98
Michelle Schatzman Toward Non Commutative Numerical
Analysis: High Order Integration in Time 99--116
L. Demkowicz and
W. Rachowicz and
Ph. Devloo A Fully Automatic $ h p $-Adaptivity . . 117--142
C. Eskilsson and
S. J. Sherwin A Discontinuous Spectral Element Model
for Boussinesq-Type Equations . . . . . 143--152
Eric Serre and
Serge Gauthier An Auto-Adaptive Multidomain Spectral
Technique for Linear Stability Analysis:
Application to Viscous Compressible
Flows . . . . . . . . . . . . . . . . . 153--165
Rick Archibald and
A. Gelb Reducing the Effects of Noise in Image
Reconstruction . . . . . . . . . . . . . 167--180
Bernhard Müller and
H. C. Yee Entropy Splitting for High Order
Numerical Simulation of Vortex Sound at
Low Mach Numbers . . . . . . . . . . . . 181--190
Cédric Chauvi\`ere and
Robert G. Owens A Robust Spectral Element Method for
Simulations of Time-Dependent
Viscoelastic Flows, Derived from the
Brownian Configuration Field Method . . 191--199
X. Escriva and
E. Leriche and
T. N. Phillips Preconditioned Uzawa Algorithm for the
Velocity--Pressure--Stress Formulation
of Viscoelastic Flow Problems . . . . . 201--210
Steven J. Ruuth and
Raymond J. Spiteri Two Barriers on
Strong-Stability-Preserving Time
Discretization Methods . . . . . . . . . 211--220
Willi Schönauer and
Torsten Adolph Higher Order May Be Better or May Not Be
Better: Investigations with the FDEM
(Finite Difference Element Method) . . . 221--229
T. Schwartzkopff and
C. D. Munz and
E. F. Toro ADER: a High-Order Approach for Linear
Hyperbolic Systems in $2$D . . . . . . . 231--240
Wendy Kress and
Bertil Gustafsson Deferred Correction Methods for Initial
Boundary Value Problems . . . . . . . . 241--251
Jirí Fürst and
Karel Kozel Application of Second Order TVD and WENO
Schemes in Internal Aerodynamics . . . . 253--262
Gabriella Puppo Numerical Entropy Production on Shocks
and Smooth Transitions . . . . . . . . . 263--271
R. Pasquetti and
C. J. Xu High-Order Algorithms for Large-Eddy
Simulation of Incompressible Flows . . . 273--284
M. M. J. Proot and
M. I. Gerritsma A Least-Squares Spectral Element
Formulation for the Stokes Problem . . . 285--296
Marc I. Gerritsma and
Michael M. J. Proot Analysis of a Discontinuous Least
Squares Spectral Element Method . . . . 297--306
Stefano Berrone and
Laurent Emmel Towards a Realization of a Wavelet
Galerkin Method on Non-Trivial Domains 307--317
M. Jardak and
C.-H. Su and
G. E. Karniadakis Spectral Polynomial Chaos Solutions of
the Stochastic Advection Equation . . . 319--338
S. J. Thomas and
R. D. Loft Semi-Implicit Spectral Element
Atmospheric Model . . . . . . . . . . . 339--350
G. Fibich and
B. Ilan and
S. Tsynkov Computation of Nonlinear Backscattering
Using a High-Order Numerical Method . . 351--364
P. Droll and
M. Schäfer A Pseudospectral Multi-Domain Method for
the Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 365--374
Alexei Lozinski and
Robert G. Owens and
Alfio Quarteroni On the Simulation of Unsteady Flow of an
Oldroyd--B Fluid by Spectral Methods . . 375--383
Huiyu Feng and
Catherine Mavriplis Adaptive Spectral Element Simulations of
Thin Premixed Flame Sheet Deformations 385--395
A. Düster and
A. Niggl and
V. Nübel and
E. Rank A Numerical Investigation of High-Order
Finite Elements for Problems of
Elastoplasticity . . . . . . . . . . . . 397--404
S. Abarbanel and
D. Gottlieb and
J. S. Hesthaven Long Time Behavior of the Perfectly
Matched Layer Equations in Computational
Electromagnetics . . . . . . . . . . . . 405--422
Moshe Goldberg and
Anna Pidgirnyak Stability Criteria for Finite Difference
Approximations to Parabolic Systems ---
an Update . . . . . . . . . . . . . . . 423--435
Yvon Maday and
Anthony T. Patera and
Gabriel Turinici A Priori Convergence Theory for
Reduced-Basis Approximations of
Single-Parameter Elliptic Partial
Differential Equations . . . . . . . . . 437--446
Yvon Maday and
Einar M. Rònquist A Reduced-Basis Element Method . . . . . 447--459
Eric Canc\`es and
Claude LeBris and
Yvon Maday and
Gabriel Turinici Towards Reduced Basis Approaches in ab
initio Electronic Structure Computations 461--469
Moshe Israeli and
Elena Braverman and
Amir Averbuch A Hierarchical $3$-D Poisson Modified
Fourier Solver by Domain Decomposition 471--479
Ruben S. Montero and
Ignacio M. Llorente and
Manuel D. Salas A Robust Multigrid Algorithm for the
Simulation of a Yawed Flat Plate . . . . 481--490
Alina Chertock and
Doron Levy A Particle Method for the KdV Equation 491--499
A. Gelb and
Z. Jackiewicz and
B. D. Welfert Absorbing Boundary Conditions of the
Second Order for the Pseudospectral
Chebyshev Methods for Wave Propagation 501--512
D. Dijkstra Doubling the Degree of Precision Without
Doubling the Grid When Solving a
Differential Equation with a
Pseudo-Spectral Collocation Method . . . 513--527
Ole F. Næss and
Knut S. Eckhoff A Modified Fourier--Galerkin Method for
the Poisson and Helmholtz Equations . . 529--539
Bertil Gustafsson and
Lina Hemmingsson-Frändén Deferred Correction in Space and Time 541--550
Arnim Brüger and
Jonas Nilsson and
Wendy Kress A Compact Higher Order Finite Difference
Method for the Incompressible
Navier--Stokes Equations . . . . . . . . 551--560
Ilaria Perugia and
Dominik Schötzau An $ h p $-Analysis of the Local
Discontinuous Galerkin Method for
Diffusion Problems . . . . . . . . . . . 561--571
Mejdi Azaiez A Spectral Element Projection Scheme for
Incompressible Flow with Application to
the Unsteady Axisymmetric Stokes Problem 573--584
Jin Xu and
Dongbin Xiu and
George Em Karniadakis A Semi-Lagrangian Method for Turbulence
Simulations Using Mixed Spectral
Discretizations . . . . . . . . . . . . 585--597
H. Joachim Schroll High Resolution Relaxed Upwind Schemes
in Gas Dynamics . . . . . . . . . . . . 599--607
V. A. Titarev and
E. F. Toro ADER: Arbitrary High Order Godunov
Approach . . . . . . . . . . . . . . . . 609--618
D. Wilhelm and
L. Kleiser Application of a Spectral Element Method
to Two-Dimensional Forward-Facing Step
Flow . . . . . . . . . . . . . . . . . . 619--627
Dan Stefanica FETI and FETI--DP Methods for Spectral
and Mortar Spectral Elements: a
Performance Comparison . . . . . . . . . 629--638
D. Weill and
M. O. Deville Steady Gap Flows by the Spectral and
Mortar Element Method . . . . . . . . . 639--648
Nicolas Fiétier and
Michel O. Deville Simulations of Time-Dependent Flows of
Viscoelastic Fluids with Spectral
Element Methods . . . . . . . . . . . . 649--657
A.-M. Matache Sparse Two-Scale FEM for Homogenization
Problems . . . . . . . . . . . . . . . . 659--669
A. W. Rüegg Implementation of Generalized Finite
Element Methods for Homogenization
Problems . . . . . . . . . . . . . . . . 671--681
L. H. Juárez and
R. Glowinski and
T. W. Pan Numerical Simulation of the
Sedimentation of Rigid Bodies in an
Incompressible Viscous Fluid by Lagrange
Multiplier/Fictitious Domain Methods
Combined with the Taylor--Hood Finite
Element Approximation . . . . . . . . . 683--694
Gennaro Coppola and
Carlo Meola Generalization of the Spline
Interpolation Based on the Principle of
the Compact Schemes . . . . . . . . . . 695--706
Leland Jameson AMR vs High Order Schemes . . . . . . . 1--24
Nejmeddine Chorfi Handling Geometric Singularities by the
Mortar Spectral Element Method I. Case
of the Laplace Equation . . . . . . . . 25--48
Xiyu Liu and
John Frazer and
Ming Xi Tang Visualization and Genetic Algorithms in
Minimax Theory for Nonlinear Functionals 49--68
Knut-Andreas Lie and
Sebastian Noelle An Improved Quadrature Rule for the
Flux-Computation in Staggered Central
Difference Schemes in Multidimensions 69--81
Sigal Gottlieb and
Lee-Ad J. Gottlieb Strong Stability Preserving Properties
of Runge--Kutta Time Discretization
Methods for Linear Constant Coefficient
Operators . . . . . . . . . . . . . . . 83--109
Mark H. Carpenter and
David Gottlieb and
Chi-Wang Shu On the Conservation and Convergence to
Weak Solutions of Global Schemes . . . . 111--132
Ken Mattsson Boundary Procedures for
Summation-by-Parts Operators . . . . . . 133--153
S. V. Tsynkov On the Definition of Surface Potentials
for Finite-Difference Operators . . . . 155--189
Huiyuan Li and
Heping Ma Shifted Chebyshev Collocation Domain
Truncation for Solving Problems on an
Infinite Interval . . . . . . . . . . . 191--213
Jan Nordström and
Rikard Gustafsson High Order Finite Difference
Approximations of Electromagnetic Wave
Propagation Close to Material
Discontinuities . . . . . . . . . . . . 215--234
YongHoon Kwon and
Ben-yu Guo and
Ki-Hyun Cha Parameter Estimation in Two-Dimensional
Space by Mixed Chebyshev--Legendre
Approximations . . . . . . . . . . . . . 235--251
Jian-Guo Liu and
Cheng Wang and
Hans Johnston A Fourth Order Scheme for Incompressible
Boussinesq Equations . . . . . . . . . . 253--285
Z. Jackiewicz and
B. D. Welfert Stability of Gauss--Radau Pseudospectral
Approximations of the One-Dimensional
Wave Equation . . . . . . . . . . . . . 287--313
H. Herrero and
S. Hoyas and
A. Donoso and
A. M. Mancho Chebyshev Collocation for a Convective
Problem in Primitive Variable
Formulation . . . . . . . . . . . . . . 315--328
Z. Chen and
R. E. Ewing Degenerate Two-Phase Incompressible Flow
IV: Local Refinement and Domain
Decomposition . . . . . . . . . . . . . 329--360
Chi-Wang Shu Foreword . . . . . . . . . . . . . . . . 1--2
R. Abgrall and
P. L. Roe High Order Fluctuation Schemes on
Triangular Meshes . . . . . . . . . . . 3--36
Tariq D. Aslam A Level Set Algorithm for Tracking
Discontinuities in Hyperbolic
Conservation Laws II: Systems of
Equations . . . . . . . . . . . . . . . 37--62
Jean-David Benamou An Introduction to Eulerian Geometrical
Optics (1992-2002) . . . . . . . . . . . 63--93
M. Bertalmio and
V. Caselles and
B. Rougé and
A. Solé TV Based Image Restoration with Local
Constraints . . . . . . . . . . . . . . 95--122
Li-Tien Cheng Construction of Shapes Arising from the
Minkowski Problem Using a Level Set
Approach . . . . . . . . . . . . . . . . 123--138
Karthikeyan Duraisamy and
James D. Baeder and
Jian-Guo Liu Concepts and Application of
Time-Limiters to High Resolution Schemes 139--162
Asghar Esmaeeli and
Grétar Tryggvason Computations of Explosive Boiling in
Microgravity . . . . . . . . . . . . . . 163--182
Frédéric Gibou and
Ronald Fedkiw and
Russel Caflisch A Level Set Approach for the Numerical
Simulation of Dendritic Growth . . . . . 183--199
X. He and
A. R. Karagozian Numerical Simulation of Pulse Detonation
Engine Phenomena . . . . . . . . . . . . 201--224
Justin Hudson and
Peter K. Sweby Formulations for Numerically
Approximating Hyperbolic Systems
Governing Sediment Transport . . . . . . 225--252
Kazufumi Ito and
Zhilin Li Solving a Nonlinear Problem in
Magneto-Rheological Fluids Using the
Immersed Interface Method . . . . . . . 253--266
Hailin Jin and
Anthony J. Yezzi and
Yen-Hsi Tsai Estimation of $3$D Surface Shape and
Smooth Radiance from $2$D Images: a
Level Set Approach . . . . . . . . . . . 267--292
Martin Kruzík and
Mitchell Luskin The Computation of Martensitic
Microstructure with Piecewise Laminates 293--308
Barry Merriman Understanding the Shu--Osher
Conservative Finite Difference Form . . 309--322
Ian M. Mitchell and
Claire J. Tomlin Overapproximating Reachable Sets by
Hamilton--Jacobi Projections . . . . . . 323--346
Audrey Rault and
Guillaume Chiavassa and
Rosa Donat Shock-Vortex Interactions at High Mach
Numbers . . . . . . . . . . . . . . . . 347--371
Steven J. Ruuth and
Brian T. R. Wetton A Simple Scheme for Volume-Preserving
Motion by Mean Curvature . . . . . . . . 373--384
Richard Sanders and
Michael Sever The Numerical Study of Singular Shocks
Regularized by Small Viscosity . . . . . 385--404
Kurt Sebastian and
Chi-Wang Shu Multidomain WENO Finite Difference
Method with Interpolation at Subdomain
Interfaces . . . . . . . . . . . . . . . 405--438
Peter Smereka Semi-Implicit Level Set Methods for
Curvature and Surface Diffusion Motion 439--456
John Steinhoff and
Meng Fan and
Lesong Wang and
William Dietz Convection of Concentrated Vortices and
Passive Scalars as Solitary Waves . . . 457--478
Mark Sussman and
M. Y. Hussaini A Discontinuous Spectral Element Method
for the Level Set Equation . . . . . . . 479--500
William W. Symes and
Jianliang Qian A Slowness Matching Eulerian Method for
Multivalued Solutions of Eikonal
Equations . . . . . . . . . . . . . . . 501--526
Anna-Karin Tornberg and
Björn Engquist Regularization Techniques for Numerical
Approximation of PDEs with Singularities 527--552
Luminita A. Vese and
Stanley J. Osher Modeling Textures with Total Variation
Minimization and Oscillating Patterns in
Image Processing . . . . . . . . . . . . 553--572
Jian-Jun Xu and
Hong-Kai Zhao An Eulerian Formulation for Solving
Partial Differential Equations Along a
Moving Interface . . . . . . . . . . . . 573--594
Z. Jackiewicz and
B. D. Welfert and
B. Zubik-Kowal Spectral Versus Pseudospectral Solutions
of the Wave Equation by Waveform
Relaxation Methods . . . . . . . . . . . 1--28
M. Svärd On Coordinate Transformations for
Summation-by-Parts Operators . . . . . . 29--42
D. C. Cole and
Y. Zou Simulation Study of Aspects of the
Classical Hydrogen Atom Interacting with
Electromagnetic Radiation: Circular
Orbits . . . . . . . . . . . . . . . . . 43--68
J. A. Carrillo and
T. Goudon A Numerical Study on Large-Time
Asymptotics of the Lifshitz--Slyozov
System . . . . . . . . . . . . . . . . . 69--113
E. Bucchignani and
D. Mansutti A Numerical Modeling of
Rayleigh-Marangoni Steady Convection in
a Non-Uniform Differentially Heated $3$D
Cavity . . . . . . . . . . . . . . . . . 115--136
Z. J. Wang and
Y. Liu Spectral (Finite) Volume Method for
Conservation Laws on Unstructured Grids
III: One Dimensional Systems and
Partition Optimization . . . . . . . . . 137--157
Jean-Paul Chehab and
Bruno Costa Time Explicit Schemes and Spatial Finite
Differences Splittings . . . . . . . . . 159--189
Micol Pennacchio The Mortar Finite Element Method for the
Cardiac ``Bidomain'' Model of
Extracellular Potential . . . . . . . . 191--210
B. Sjögreen and
H. C. Yee Multiresolution Wavelet Based Adaptive
Numerical Dissipation Control for High
Order Methods . . . . . . . . . . . . . 211--255
Phu Luong and
Clay P. Breshears and
Le N. Ly Application of Multiblock Grid and
Dual-Level Parallelism in Coastal Ocean
Circulation Modeling . . . . . . . . . . 257--275
Weifu Fang and
Yi Wang and
Yuesheng Xu An Implementation of Fast Wavelet
Galerkin Methods for Integral Equations
of the Second Kind . . . . . . . . . . . 277--302
Ke Li and
Zi-Niu Wu Nonet--Cartesian Grid Method for Shock
Flow Computations . . . . . . . . . . . 303--329
Karl Hörnell and
Per Lötstedt Adaptive Iteration to Steady State of
Flow Problems . . . . . . . . . . . . . 331--354
J. M. Bernard Spectral Discretizations of the Stokes
Equations with Non Standard Boundary
Conditions . . . . . . . . . . . . . . . 355--377
Daniel C. Cole and
Yi Zou Simulation Study of Aspects of the
Classical Hydrogen Atom Interacting with
Electromagnetic Radiation: Elliptical
Orbits . . . . . . . . . . . . . . . . . 379--404
Adour V. Kabakian and
Vijaya Shankar and
William F. Hall Unstructured Grid-Based Discontinuous
Galerkin Method for Broadband
Electromagnetic Simulations . . . . . . 405--431
Anne Gelb Parameter Optimization and Reduction of
Round Off Error for the Gegenbauer
Reconstruction Method . . . . . . . . . 433--459
Anonymous Erratum: Application of Multiblock Grid
and Dual-Level Parallelism in Coastal
Ocean Circulation Modeling . . . . . . . 461--462
F. Bouchut An Antidiffusive Entropy Scheme for
Monotone Scalar Conservation Laws . . . 1--30
R. Li and
W. B. Liu and
H. P. Ma Moving Mesh Method with
Error-Estimator-Based Monitor and Its
Applications to Static Obstacle Problem 31--55
Ken Mattsson and
Magnus Svärd and
Jan Nordström Stable and Accurate Artificial
Dissipation . . . . . . . . . . . . . . 57--79
Wilhelm Heinrichs Least-Squares Spectral Collocation for
the Navier--Stokes Equations . . . . . . 81--90
Elena Braverman and
Boris Epstein and
Moshe Israeli A Fast Spectral Subtractional Solver for
Elliptic Equations . . . . . . . . . . . 91--128
P. Alexander High Order Computation of the History
Term in the Equation of Motion for a
Spherical Particle in a Fluid . . . . . 129--143
Daniel C. Cole and
Yi Zou Perturbation Analysis and Simulation
Study of the Effects of Phase on the
Classical Hydrogen Atom Interacting with
Circularly Polarized Electromagnetic
Radiation . . . . . . . . . . . . . . . 145--172
J. L. V. Lewandowski Particle-in-Cell Simulations with
Kinetic Electrons . . . . . . . . . . . 173--192
Inmaculada Higueras On Strong Stability Preserving Time
Discretization Methods . . . . . . . . . 193--223
T. K. Sengupta and
A. Dipankar A Comparative Study of Time Advancement
Methods for Solving Navier--Stokes
Equations . . . . . . . . . . . . . . . 225--250
H. Joachim Schroll Relaxed High Resolution Schemes for
Hyperbolic Conservation Laws . . . . . . 251--279
Pierre Sagaut Foreword . . . . . . . . . . . . . . . . 251--251
Tapan K. Sengupta and
G. Ganerwal and
Anurag Dipankar High Accuracy Compact Schemes and Gibbs'
Phenomenon . . . . . . . . . . . . . . . 253--268
Tapan K. Sengupta and
A. Guntaka and
S. Dey Navier--Stokes Solution by New Compact
Scheme for Incompressible Flows . . . . 269--282
Ali Uzun and
Gregory A. Blaisdell and
Anastasios S. Lyrintzis Application of Compact Schemes to Large
Eddy Simulation of Turbulent Jets . . . 283--319
Xiangang Zhang and
Gregory A. Blaisdell High-Order Compact Schemes with Filters
on Multi-block Domains . . . . . . . . . 321--339
Tim Broeckhoven and
Sergey Smirnov and
Jan Ramboer Finite Volume Formulation of Compact
Upwind and Central Schemes with
Artificial Selective Damping . . . . . . 341--367
J. Monnier and
P. Witomski Analysis of a Local Hydrodynamic Model
with Marangoni Effect . . . . . . . . . 369--403
A. Rousseau and
R. Temam and
J. Tribbia Boundary Layers in an Ocean Related
System . . . . . . . . . . . . . . . . . 405--432
Anonymous Foreword . . . . . . . . . . . . . . . . 1--2
Slimane Adjerid and
Andreas Klauser Superconvergence of Discontinuous Finite
Element Solutions for Transient
Convection-diffusion Problems . . . . . 5--24
Douglas N. Arnold and
Franco Brezzi and
L. Donatella Marini A Family of Discontinuous Galerkin
Finite Elements for the
Reissner--Mindlin Plate . . . . . . . . 25--45
Onno Bokhove Flooding and Drying in Discontinuous
Galerkin Finite-Element Discretizations
of Shallow-Water Equations. Part 1: One
Dimension . . . . . . . . . . . . . . . 47--82
Susanne C. Brenner and
Li-Yeng Sung $ C^0 $ Interior Penalty Methods for
Fourth Order Elliptic Boundary Value
Problems on Polygonal Domains . . . . . 83--118
F. Brezzi and
T. J. R. Hughes and
L. D. Marini and
A. Masud Mixed Discontinuous Galerkin Methods for
Darcy Flow . . . . . . . . . . . . . . . 119--145
Rommel Bustinza and
Gabriel N. Gatica and
Bernardo Cockburn An A Posteriori Error Estimate for the
Local Discontinuous Galerkin Method
Applied to Linear and Nonlinear
Diffusion Problems . . . . . . . . . . . 147--185
Paul Castillo An A Posteriori Error Estimate for the
Local Discontinuous Galerkin Method . . 187--204
Min-Hung Chen and
Bernardo Cockburn and
Fernando Reitich High-order RKDG Methods for
Computational Electromagnetics . . . . . 205--226
N. Chevaugeon and
J. Xin and
P. Hu and
X. Li and
D. Cler Discontinuous Galerkin Methods Applied
to Shock and Blast Problems . . . . . . 227--243
Clint Dawson and
Vadym Aizinger A Discontinuous Galerkin Method for
Three-Dimensional Shallow Water
Equations . . . . . . . . . . . . . . . 245--267
C. Eskilsson and
S. J. Sherwin Discontinuous Galerkin Spectral/$ h p $
Element Modelling of Dispersive Shallow
Water Systems . . . . . . . . . . . . . 269--288
Xiaobing Feng and
Ohannes A. Karakashian Two-Level Non-Overlapping Schwarz
Preconditioners for a Discontinuous
Galerkin Approximation of the Biharmonic
Equation . . . . . . . . . . . . . . . . 289--314
Paul Houston and
Ilaria Perugia and
Dominik Schötzau Mixed Discontinuous Galerkin
Approximation of the Maxwell Operator:
Non-Stabilized Formulation . . . . . . . 315--346
Houston Paul and
Dominik Schötzau and
Thomas P. Wihler Energy Norm shape A Posteriori Error
Estimation for Mixed Discontinuous
Galerkin Approximations of the Stokes
Problem . . . . . . . . . . . . . . . . 347--370
Kanschat Guido Block Preconditioners for LDG
Discretizations of Linear Incompressible
Flow Problems . . . . . . . . . . . . . 371--384
Robert M. Kirby and
George Em Karniadakis Selecting the Numerical Flux in
Discontinuous Galerkin Methods for
Diffusion Problems . . . . . . . . . . . 385--411
Fengyan Li and
Chi-Wang Shu Locally Divergence-Free Discontinuous
Galerkin Methods for MHD Equations . . . 413--442
Peter Monk and
Gerard R. Richter A Discontinuous Galerkin Method for
Linear Symmetric Hyperbolic Systems in
Inhomogeneous Media . . . . . . . . . . 443--477
Béatrice Riviére Analysis of a Discontinuous Finite
Element Method for the Coupled Stokes
and Darcy Problems . . . . . . . . . . . 479--500
Shuyu Sun and
Mary F. Wheeler $ L^2 $ ($ H^1 $ Norm) A Posteriori
Error Estimation for Discontinuous
Galerkin Approximations of Reactive
Transport Problems . . . . . . . . . . . 501--530
J. J. W. van der Vegt and
S. K. Tomar Discontinuous Galerkin Method for Linear
Free-Surface Gravity Waves . . . . . . . 531--567
Chi-Wang Shu and
Wai-Sun Don and
David Gottlieb Numerical Convergence Study of Nearly
Incompressible, Inviscid Taylor--Green
Vortex Flow . . . . . . . . . . . . . . 1--27
Youngsoo Ha and
Carl L. Gardner and
Anne Gelb and
Chi-Wang Shu Numerical Simulation of High Mach Number
Astrophysical Jets with Radiative
Cooling . . . . . . . . . . . . . . . . 29--44
James W. Lottes and
Paul F. Fischer Hybrid Multigrid/Schwarz Algorithms for
the Spectral Element Method . . . . . . 45--78
Magnus Svärd and
Ken Mattsson and
Jan Nordström Steady-State Computations Using
Summation-by-Parts Operators . . . . . . 79--95
Inmaculada Higueras Monotonicity for Runge--Kutta Methods:
Inner Product Norms . . . . . . . . . . 97--117
Tao Tang and
Andy Wathen Preface . . . . . . . . . . . . . . . . 119--119
Xiaobing Feng and
Hai-jun Wu A Posteriori Error Estimates and an
Adaptive Finite Element Method for the
Allen--Cahn Equation and the Mean
Curvature Flow . . . . . . . . . . . . . 121--146
M. A. Walkley and
P. H. Gaskell and
P. K. Jimack Finite Element Simulation of
Three-Dimensional Free-Surface Flow
Problems . . . . . . . . . . . . . . . . 147--162
Keith Miller Stabilized Moving Finite Elements for
Convection Dominated Problems . . . . . 163--182
Li-Lian Wang and
Jie Shen Error Analysis for Mapped Jacobi
Spectral Methods . . . . . . . . . . . . 183--218
Yves Tourigny The Optimisation of the Mesh in
First-Order Systems Least-Squares
Methods . . . . . . . . . . . . . . . . 219--245
Anotida Madzvamuse and
Philip K. Maini and
Andrew J. Wathen A Moving Grid Finite Element Method for
the Simulation of Pattern Generation by
Turing Models on Growing Domains . . . . 247--262
Paul A. Zegeling On Resistive MHD Models with Adaptive
Moving Meshes . . . . . . . . . . . . . 263--284
E. F. Toro and
V. A. Titarev TVD Fluxes for the High-Order ADER
Schemes . . . . . . . . . . . . . . . . 285--309
S. Cordier and
B. Lucquin-Desreux and
S. Mancini Focalization: a Numerical Test for
Smoothing Effects of Collision Operators 311--320
Ruo Li On Multi-Mesh $H$-Adaptive Methods . . . 321--341
Weiming Cao and
Ronald D. Haynes and
Manfred R. Trummer Preconditioning for a Class of Spectral
Differentiation Matrices . . . . . . . . 343--371
Steven A. Orszag and
Isaac Goldhirsch and
Sudhir Srinivasan `Perfectly' Scalable Data I/O . . . . . 373--404
Mark H. Carpenter and
David I. Gottlieb and
Jan S. Hesthaven Foreword . . . . . . . . . . . . . . . . 1--2
L. F. Shampine Error Estimation and Control for ODEs 3--16
C. William Gear and
Ioannis G. Kevrekidis Constraint-Defined Manifolds: a Legacy
Code Approach to Low-Dimensional
Computation . . . . . . . . . . . . . . 17--28
Z. Jackiewicz Construction and Implementation of
General Linear Methods for Ordinary
Differential Equations: a Review . . . . 29--49
J. C. Butcher High Order $A$-stable Numerical Methods
for Stiff Problems . . . . . . . . . . . 51--66
Ernst Hairer Important Aspects of Geometric Numerical
Integration . . . . . . . . . . . . . . 67--81
U. M. Ascher and
R. I. McLachlan On Symplectic and Multisymplectic
Schemes for the KdV Equation . . . . . . 83--104
Sigal Gottlieb On High Order Strong Stability
Preserving Runge--Kutta and Multi Step
Time Discretizations . . . . . . . . . . 105--128
Lorenzo Pareschi and
Giovanni Russo Implicit-Explicit Runge--Kutta Schemes
and Applications to Hyperbolic Systems
with Relaxation . . . . . . . . . . . . 129--155
M. H. Carpenter and
C. A. Kennedy and
Hester Bijl and
S. A. Viken Fourth-Order Runge--Kutta Schemes for
Fluid Mechanics Applications . . . . . . 157--194
Bertil Gustafsson and
Per Wahlund Time Compact High Order Difference
Methods for Wave Propagation, $2$D . . . 195--211
D. A. Knoll and
V. A. Mousseau and
L. Chacón and
J. Reisner Jacobian-Free Newton--Krylov Methods for
the Accurate Time Integration of Stiff
Wave Systems . . . . . . . . . . . . . . 213--230
S. Faure and
J. Laminie and
R. Temam Finite Volume Discretization and
Multilevel Methods in Flow Problems . . 231--261
H. N. Najm and
O. M. Knio Modeling Low Mach Number Reacting Flow
with Detailed Chemistry and Transport 263--287
J. S. Shang Solving Schemes for Computational
Magneto-Aerodynamics . . . . . . . . . . 289--306
S. J. Thomas and
R. D. Loft The NCAR Spectral Element Climate
Dynamical Core: Semi-Implicit Eulerian
Formulation . . . . . . . . . . . . . . 307--322
D. Xiu and
S. J. Sherwin and
S. Dong and
G. E. Karniadakis Strong and Auxiliary Forms of the
Semi-Lagrangian Method for
Incompressible Flows . . . . . . . . . . 323--346
H. C. Elman Preconditioning Strategies for Models of
Incompressible Flow . . . . . . . . . . 347--366
Jae-Hun Jung and
Bernie D. Shizgal Inverse Polynomial Reconstruction of Two
Dimensional Fourier Images . . . . . . . 367--399
Konstantinos Chrysafinos Moving Mesh Finite Element Methods for
an Optimal Control Problem for the
Advection--Diffusion Equation . . . . . 401--421
Philippe Guillaume and
Vladimir Latocha Numerical Convergence of a
Parameterisation Method for the Solution
of a Highly Anisotropic Two-Dimensional
Elliptic Problem . . . . . . . . . . . . 423--444
A. Debussche and
J. Laminie and
E. Zahrouni A Dynamical Multi-level Scheme for the
Burgers Equation: Wavelet and
Hierarchical Finite Element . . . . . . 445--497
P. A. Reiser Calculation of Lossy Dielectric
Multilayer Filter Response . . . . . . . 499--513
Scot Adams and
Bernardo Cockburn A Mixed Finite Element Method for
Elasticity in Three Dimensions . . . . . 515--521
Thomas P. Wihler An a Priori Error Analysis of the $ h p
$-Version of the Continuous Galerkin FEM
for Nonlinear Initial Value Problems . . 523--549
Jichun Li and
Miguel R. Visbal High-order Compact Schemes for Nonlinear
Dispersive Waves . . . . . . . . . . . . 1--23
E. Leriche and
E. Perchat and
G. Labrosse and
M. O. Deville Numerical Evaluation of the Accuracy and
Stability Properties of High-order
Direct Stokes Solvers with or without
Temporal Splitting . . . . . . . . . . . 25--43
Ercília Sousa Stability Analysis of Difference Methods
for Parabolic Initial Value Problems . . 45--66
Saul Abarbanel and
Adi Ditkowski and
Amir Yefet Bounded Error Schemes for the Wave
Equation on Complex Domains . . . . . . 67--81
Lars Ferm and
Per Lötstedt Space-Time Adaptive Solution of First
Order PDES . . . . . . . . . . . . . . . 83--110
A. Nersessian and
A. Poghosyan On a Rational Linear Approximation of
Fourier Series for Smooth Functions . . 111--125
Shi Jin and
Chunxiong Zheng A Time-Splitting Spectral Method for the
Generalized Zakharov System in
Multi-Dimensions . . . . . . . . . . . . 127--149
T. K. Sengupta and
S. K. Sircar and
A. Dipankar High Accuracy Schemes for DNS and
Acoustics . . . . . . . . . . . . . . . 151--193
Jonas Koko Uzawa Conjugate Gradient Domain
Decomposition Methods for Coupled Stokes
Flows . . . . . . . . . . . . . . . . . 195--216
Tao Feng and
Mårten Gulliksson and
Wenbin Liu Adaptive Finite Element Methods for the
Identification of Elastic Constants . . 217--235
H. J. Schroll and
F. Svensson A Bi-Hyperbolic Finite Volume Method on
Quadrilateral Meshes . . . . . . . . . . 237--260
Michael B. Nielsen and
Ken Museth Dynamic Tubular Grid: an Efficient Data
Structure and Algorithms for High
Resolution Level Sets . . . . . . . . . 261--299
David A. Kopriva Metric Identities and the Discontinuous
Spectral Element Method on Curvilinear
Meshes . . . . . . . . . . . . . . . . . 301--327
Stefan Jakobsson Frequency Optimized Computation Methods 329--362
David Gottlieb and
Jan S. Hesthaven and
George Karniadakis Foreword . . . . . . . . . . . . . . . . 1--3
M. Ainsworth and
P. Monk and
W. Muniz Dispersive and Dissipative Properties of
Discontinuous Galerkin Finite Element
Methods for the Second-Order Wave
Equation . . . . . . . . . . . . . . . . 5--40
M. Aza\"\iez and
R. Gruber and
M. O. Deville and
E. H. Mund On a Stable Spectral Method for the
grad(div) Eigenvalue Problem . . . . . . 41--50
Luca F. Pavarino and
Elena Zampieri Overlapping Schwarz and Spectral Element
Methods for Linear Elasticity and
Elastic Waves . . . . . . . . . . . . . 51--73
Eugene Kashdan and
Eli Turkel A High-Order Accurate Method for
Frequency Domain Maxwell Equations with
Discontinuous Coefficients . . . . . . . 75--95
Z. Belhachmi and
C. Bernardi and
S. Deparis and
F. Hecht An Efficient Discretization of the
Navier--Stokes Equations in an
Axisymmetric Domain. Part 1: The
Discrete Problem and its Numerical
Analysis . . . . . . . . . . . . . . . . 97--110
Z. Belhachmi and
A. Karageorghis and
K. Taous Identification and Reconstruction of a
Small Leak Zone in a Pipe by a Spectral
Element Method . . . . . . . . . . . . . 111--122
N. Bodard and
M. O. Deville Fluid-Structure Interaction by the
Spectral Element Method . . . . . . . . 123--136
Roland Bouffanais and
Michel O. Deville Mesh Update Techniques for Free-Surface
Flow Solvers Using Spectral Element
Method . . . . . . . . . . . . . . . . . 137--149
Roland Bouffanais and
Michel O. Deville and
Paul F. Fischer Large-Eddy Simulation of the Lid-Driven
Cubic Cavity Flow by the Spectral
Element Method . . . . . . . . . . . . . 151--162
Steve Bryson and
Doron Levy On the Total Variation of High-Order
Semi-Discrete Central Schemes for
Conservation Laws . . . . . . . . . . . 163--175
Fatih Celiker and
Bernardo Cockburn Element-by-Element Post-Processing of
Discontinuous Galerkin Methods for
Timoshenko Beams . . . . . . . . . . . . 177--187
Alina Chertock and
Alexander Kurganov and
Guergana Petrova Finite-Volume-Particle Methods for
Models of Transport of Pollutant in
Shallow Water . . . . . . . . . . . . . 189--199
Bart De Maerschalck and
Marc I. Gerritsma Higher-Order Gauss--Lobatto Integration
for Non-Linear Hyperbolic Equations . . 201--214
Michael Dumbser and
Claus-Dieter Munz Building Blocks for Arbitrary High Order
Discontinuous Galerkin Schemes . . . . . 215--230
Huiyu Feng and
Catherine Mavriplis and
Rob Van der Feng Parallel $3$D Mortar Element Method for
Adaptive Nonconforming Meshes . . . . . 231--243
Marc I. Gerritsma Direct Minimization of the Discontinuous
Least-Squares Spectral Element Method
for Viscoelastic Fluids . . . . . . . . 245--256
Paola Gervasio and
Fausto Saleri Algebraic Fractional-Step Schemes for
Time-Dependent Incompressible
Navier--Stokes Equations . . . . . . . . 257--269
Sigal Gottlieb and
Julia S. Mullen and
Steven J. Ruuth A Fifth Order Flux Implicit WENO Method 271--287
Sigal Gottlieb and
Steven J. Ruuth Optimal Strong-Stability-Preserving
Time-Stepping Schemes with Fast Downwind
Spatial Discretizations . . . . . . . . 289--303
Ben-Yu Guo and
Jie Shen and
Li-Lian Wang Optimal Spectral--Galerkin Methods Using
Generalized Jacobi Polynomials . . . . . 305--322
Alexander Kurganov and
Guergana Petrova Adaptive Central-Upwind Schemes for
Hamilton--Jacobi Equations with
Nonconvex Hamiltonians . . . . . . . . . 323--333
Emmanuel Leriche Direct Numerical Simulation in a
Lid-Driven Cubical Cavity at High
Reynolds Number by a Chebyshev Spectral
Method . . . . . . . . . . . . . . . . . 335--345
Ruo Li and
Tao Tang Moving Mesh Discontinuous Galerkin
Method for Hyperbolic Conservation Laws 347--363
Richard Pasquetti Spectral Vanishing Viscosity Method for
Large-Eddy Simulation of Turbulent Flows 365--375
Richard Pasquetti and
Francesca Rapetti Spectral Element Methods on Unstructured
Meshes: Comparisons and Recent Advances 377--387
Michael M. J. Proot and
Marc I. Gerritsma Mass- and Momentum Conservation of the
Least-Squares Spectral Element Method
for the Stokes Problem . . . . . . . . . 389--401
Gabriella Puppo and
Giovanni Russo Staggered Finite Difference Schemes for
Conservation Laws . . . . . . . . . . . 403--418
Ivan L. Sofronov and
Olga V. Podgornova A Spectral Approach for Generating
Non-Local Boundary Conditions for
External Wave Problems in Anisotropic
Media . . . . . . . . . . . . . . . . . 419--430
Erik Stålberg and
Arnim Brüger and
Per Lötstedt High Order Accurate Solution of Flow
Past a Circular Cylinder . . . . . . . . 431--441
Chris Talbot and
Andrew Crampton Pseudo Spectral Methods Applied to
Problems in Elasticity . . . . . . . . . 443--454
Xiaoliang Wan and
George Em Karniadakis Beyond Wiener--Askey Expansions:
Handling Arbitrary PDFs . . . . . . . . 455--464
Christos Xenophontos The Use of Curved Elements in the Finite
Element Approximation of Thin Plates by
High Order $p$ and $ h p $ Methods . . . 465--476
Yulong Xing and
Chi-Wang Shu High-Order Well-Balanced Finite
Difference WENO Schemes for a Class of
Hyperbolic Systems with Source Terms . . 477--494
Chuanju Xu Stabilization Methods for Spectral
Element Computations of Incompressible
Flows . . . . . . . . . . . . . . . . . 495--505
H. C. Yee and
B. Sjögreen Non-Linear Filtering and Limiting in
High Order Methods for Ideal and
Non-Ideal MHD . . . . . . . . . . . . . 507--521
Zhang Xiao-yong and
Guo Ben-yu Spherical Harmonic-Generalized Laguerre
Spectral Method for Exterior Problems 523--537
Matthew Brown and
Margot Gerritsen An Energy-Stable High-Order Central
Difference Scheme for the
Two-Dimensional Shallow Water Equations 1--30
Th. Tsangaris and
Y.-S. Smyrlis and
A. Karageorghis A Matrix Decomposition MFS Algorithm for
Problems in Hollow Axisymmetric Domains 31--50
Peter Benner and
Enrique S. Quintana-Ortí Solving Stable Sylvester Equations via
Rational Iterative Schemes . . . . . . . 51--83
Liu Yan and
Mao De-kang Further Development of a Conservative
Front-Tracking Method for Systems of
Conservation Laws in One Space Dimension 85--119
Saul Abarbanel Introduction . . . . . . . . . . . . . . 121--123
S. Abarbanel and
D. Gottlieb and
J. S. Hesthaven Non-Linear PML Equations for Time
Dependent Electromagnetics in Three
Dimensions . . . . . . . . . . . . . . . 125--137
Valery Agoshkov and
Alfio Quarteroni and
Gianluigi Rozza A Mathematical Approach in the Design of
Arterial Bypass Using Unsteady Stokes
Equations . . . . . . . . . . . . . . . 139--165
Rick Archibald and
Anne Gelb and
Sigal Gottlieb and
Jennifer Ryan One-sided Post-processing for the
Discontinuous Galerkin Method Using ENO
Type Stencil Choosing and the Local Edge
Detection Method . . . . . . . . . . . . 167--190
H. T. Banks and
V. A. Bokil and
D. Cioranescu and
N. L. Gibson Homogenization of Periodically Varying
Coefficients in Electromagnetic
Materials . . . . . . . . . . . . . . . 191--221
Claudio Canuto Enhanced Coercivity for Pure Advection
and Advection--Diffusion Problems . . . 223--244
Alexandre J. Chorin and
Ole H. Hald and
Raz Kupferman Prediction from Partial Data,
Renormalization, and Averaging . . . . . 245--261
Min Hyung Cho and
Wei Cai and
Tsing-Hua Her A Boundary Integral Equation Method for
Photonic Crystal Fibers . . . . . . . . 263--278
A. Gelb and
E. Tadmor Adaptive Edge Detectors for Piecewise
Smooth Data Based on the minmod Limiter 279--306
Sigal Gottlieb and
David Gottlieb and
Chi-Wang Shu Recovering High-Order Accuracy in WENO
Computations of Steady-State Hyperbolic
Systems . . . . . . . . . . . . . . . . 307--318
Bertil Gustafsson and
Yaser Khalighi The Shifted Box Scheme for Scalar
Transport Problems . . . . . . . . . . . 319--335
J. S. Hesthaven and
S. M. Kaber and
L. Lurati Padé--Legendre Interpolants for Gibbs
Reconstruction . . . . . . . . . . . . . 337--359
Chang-Yeol Jung and
Roger Temam On Parabolic Boundary Layers for
Convection--Diffusion Equations in a
Channel: Analysis and Numerical
Applications . . . . . . . . . . . . . . 361--410
Stefan Kindermann and
Stanley Osher and
Jinjun Xu Denoising by BV-duality . . . . . . . . 411--444
Peter D. Lax Gibbs Phenomena . . . . . . . . . . . . 445--449
Yvon Maday $ L^\infty $-Stable Approximation of a
Solution to $ {\rm Div}(Y) = f $ for $ f
\in L^2 $ in Two Dimensions . . . . . . 451--458
Steven A. Orszag and
Hudong Chen and
Sauro Succi and
Jonas Latt Turbulence Effects on Kinetic Equations 459--466
V. Ryaben'kii On the Method of Difference Potentials 467--478
M. D. Salas Digital Flight: The Last CFD
Aeronautical Grand Challenge . . . . . . 479--505
J. S. Shang Simulating Plasma Microwave Diagnostics 507--532
Stefan Turek and
Ludmila Rivkind and
Jaroslav Hron Numerical Study of a Modified
Time-Stepping $ \theta $-Scheme for
Incompressible Flow Simulations . . . . 533--547
E. Turkel Numerical Methods and Nature . . . . . . 549--570
John P. Boyd Asymptotic Fourier Coefficients for a $
C_\infty $ Bell (Smoothed-``Top-Hat'') &
the Fourier Extension Problem . . . . . 1--24
Yong-Tao Zhang and
Hong-Kai Zhao and
Jianliang Qian High Order Fast Sweeping Methods for
Static Hamilton--Jacobi Equations . . . 25--56
Susana Serna and
Jianliang Qian Fifth-Order Weighted Power--ENO Schemes
for Hamilton--Jacobi Equations . . . . . 57--81
Steinar Evje and
Tore Flåtten CFL-Violating Numerical Schemes for a
Two-Fluid Model . . . . . . . . . . . . 83--114
H. C. Yee and
Björn Sjögreen Efficient Low Dissipative High Order
Schemes for Multiscale MHD Flows, II:
Minimization of $ \Delta \cdot B $
Numerical Error . . . . . . . . . . . . 115--164
P. Morgan and
M. Visbal and
D. Rizzetta A Parallel Overset Grid High-Order Flow
Solver for Large Eddy Simulation . . . . 165--200
A. Y. Suhov A Spectral Method for the Time Evolution
in Parabolic Problems . . . . . . . . . 201--217
Silvia Bertoluzza and
Silvia Falletta and
Valérie Perrier Implementation of the Mortar Method in
the Wavelet Context . . . . . . . . . . 219--255
Daniel Goujot Blind Wavelet Compression of the
Solution of a Nonlinear PDE with
Singular Forcing Term Within Optimal
Order Cost: Stability of Restricted
Approximation to Small Errors . . . . . 257--297
Qian-Yong Chen Partitions for Spectral (Finite) Volume
Reconstruction in the Tetrahedron . . . 299--319
John B. Greer An Improvement of a Recent Eulerian
Method for Solving PDEs on General
Geometries . . . . . . . . . . . . . . . 321--352
Hailiang Liu and
Li-Tien Cheng and
Stanley Osher A Level Set Framework for Capturing
Multi-Valued Solutions of Nonlinear
First-Order Equations . . . . . . . . . 353--373
Jan Nordström Conservative Finite Difference
Formulations, Variable Coefficients,
Energy Estimates and Artificial
Dissipation . . . . . . . . . . . . . . 375--404
Olivier Bokanowski and
Hasnaa Zidani Anti-Dissipative Schemes for Advection
and Application to
Hamilton--Jacobi--Bellmann Equations . . 1--33
Henrik Brandén and
Sverker Holmgren and
Per Sundqvist Discrete Fundamental Solution
Preconditioning for Hyperbolic Systems
of PDE . . . . . . . . . . . . . . . . . 35--60
Zhilin Li and
C. V. Pao and
Zhonghua Qiao A Finite Difference Method and Analysis
for $2$D Nonlinear Poisson--Boltzmann
Equations . . . . . . . . . . . . . . . 61--81
David E. Amundsen and
Oscar Bruno Time Stepping Via One-Dimensional Padé
Approximation . . . . . . . . . . . . . 83--115
Jinhai Chen and
Weiguo Li Equivalent Conditions for Convergence of
Splittings of Non-Hermitian Indefinite
Matrices . . . . . . . . . . . . . . . . 117--130
R. Abgrall and
F. Marpeau Residual Distribution Schemes on
Quadrilateral Meshes . . . . . . . . . . 131--175
G. B. Jacobs and
D. A. Kopriva and
F. Mashayek A Conservative Isothermal Wall Boundary
Condition for the Compressible
Navier--Stokes Equations . . . . . . . . 177--192
Robert Artebrant Third Order Accurate Non-Polynomial
Reconstruction on Rectangular and
Triangular Meshes . . . . . . . . . . . 193--221
Frank Haußer and
Axel Voigt A Discrete Scheme for Parametric
Anisotropic Surface Diffusion . . . . . 223--235
Matthias K. Gobbert and
Samuel G. Webster and
Timothy S. Cale A Galerkin Method for the Simulation of
the Transient $2$-D/$2$-D and
$3$-D/$3$-D Linear Boltzmann Equation 237--273
Zakaria Belhachmi and
Andreas Karageorghis A Spectral Mortar Element Discretization
of the Poisson Equation with Mixed
Boundary Conditions . . . . . . . . . . 275--299
W. H. Hui and
Z. N. Wu and
B. Gao Preliminary Extension of the Unified
Coordinate System Approach to
Computation of Viscous Flows . . . . . . 301--344
Jianxian Qiu A Numerical Comparison of the
Lax--Wendroff Discontinuous Galerkin
Method Based on Different Numerical
Fluxes . . . . . . . . . . . . . . . . . 345--367
Francesca Tosi and
Stefano Ubertini and
S. Succi and
I. V. Karlin Optimization Strategies for the Entropic
Lattice Boltzmann Method . . . . . . . . 369--387
Y. V. S. S. Sanyasiraju and
V. Manjula Fourth-Order Semi-Compact Scheme for
Flow Past a Rotating and Translating
Cylinder . . . . . . . . . . . . . . . . 389--407
Anne Gelb Reconstruction of Piecewise Smooth
Functions from Non-uniform Grid Point
Data . . . . . . . . . . . . . . . . . . 409--440
Arne Taube and
Michael Dumbser and
Dinshaw S. Balsara Arbitrary High-Order Discontinuous
Galerkin Schemes for the
Magnetohydrodynamic Equations . . . . . 441--464
Igor Mozolevski and
Endre Süli and
Paulo R. Bösing $ h p $-Version a priori Error Analysis
of Interior Penalty Discontinuous
Galerkin Finite Element Approximations
to the Biharmonic Equation . . . . . . . 465--491
Siegfried Müller and
Youssef Stiriba Fully Adaptive Multiscale Schemes for
Conservation Laws Employing Locally
Varying Time Stepping . . . . . . . . . 493--531
Ellen M. Taylor and
M. Pino Martín Stencil Adaptation Properties of a WENO
Scheme in Direct Numerical Simulations
of Compressible Turbulence . . . . . . . 533--554
Stanley Osher Preface . . . . . . . . . . . . . . . . 1--3
L. A. Cafferelli and
Fang Hua Lin An Optimal Partition Problem for
Eigenvalues . . . . . . . . . . . . . . 5--18
Han Chen and
Chohong Min and
Frédéric Gibou A Supra-Convergent Finite Difference
Scheme for the Poisson and Heat
Equations on Irregular Domains and
Non-Graded Adaptive Cartesian Grids . . 19--60
Bernardo Cockburn and
Guido Kanschat and
Dominik Schötzau A Note on Discontinuous Galerkin
Divergence-free Solutions of the
Navier--Stokes Equations . . . . . . . . 61--73
Yana Di and
Ruo Li and
Tao Tang and
Pingwen Zhang Level Set Calculations for
Incompressible Two-Phase Flows on a
Dynamically Adaptive Grid . . . . . . . 75--98
Jeong-Mo Hong and
Tamar Shinar and
Myungjoo Kang On Boundary Condition Capturing for
Multiphase Interfaces . . . . . . . . . 99--125
Songming Hou and
Xu-Dong Liu Solutions of Multi-dimensional
Hyperbolic Systems of Conservation Laws
by Square Entropy Condition Satisfying
Discontinuous Galerkin Method . . . . . 127--151
Myungjoo Kang and
Hyeseon Shim and
Stanley Osher Level Set Based Simulations of Two-Phase
Oil--Water Flows in Pipes . . . . . . . 153--184
Peter D. Lax Computational Fluid Dynamics . . . . . . 185--193
Chi-Tien Lin and
Xu-Dong Liu Convex ENO Schemes for Hamilton--Jacobi
Equations . . . . . . . . . . . . . . . 195--211
Jinjie Liu and
Hyun-Kyung Lim and
James Glimm and
Xiaolin Li A Conservative Front Tracking Method in
$N$-Dimensions . . . . . . . . . . . . . 213--236
Jianliang Qian and
Yong-Tao Zhang and
Hong-Kai Zhao A Fast Sweeping Method for Static Convex
Hamilton--Jacobi Equations . . . . . . . 237--271
Shuhai Zhang and
Chi-Wang Shu A New Smoothness Indicator for the WENO
Schemes and Its Effect on the
Convergence to Steady State Solutions 273--305
T. Z. Boulmezaoud and
J. M. Urquiza On The Eigenvalues of the Spectral
Second Order Differentiation Operator
and Application to the Boundary
Observability of the Wave Equation . . . 307--345
Christophe Berthon and
Pierre Charrier and
Bruno Dubroca An HLLC Scheme to Solve The $ M_1 $
Model of Radiative Transfer in Two Space
Dimensions . . . . . . . . . . . . . . . 347--389
Avram Sidi A Novel Class of Symmetric and
Nonsymmetric Periodizing Variable
Transformations for Numerical
Integration . . . . . . . . . . . . . . 391--417
François Alouges and
Gérard Le Coq and
Emmanuel Lorin Two-Dimensional Extension of the
Reservoir Technique for Some Linear
Advection Systems . . . . . . . . . . . 419--458
Sandra Pieraccini and
Gabriella Puppo Implicit-Explicit Schemes for BGK
Kinetic Equations . . . . . . . . . . . 1--28
Adi Ditkowski and
Gadi Fibich and
Nir Gavish Efficient Solution of $A$, $ x^{(k)} =
b^{(k)} $ Using $ A^{-1} $ . . . . . . . 29--44
Z. J. Wang and
Yen Liu and
Georg May and
Antony Jameson Spectral Difference Method for
Unstructured Grids II: Extension to the
Euler Equations . . . . . . . . . . . . 45--71
Petr Kloucek and
Danny C. Sorensen and
Jennifer L. Wightman The Approximation and Computation of a
Basis of the Trace Space $ H^{1 / 2} $ 73--108
Peter Diener and
Ernst Nils Dorband and
Erik Schnetter Optimized High-Order Derivative and
Dissipation Operators Satisfying
Summation by Parts, and Applications in
Three-dimensional Multi-block Evolutions 109--145
Katsushi Ohmori and
Norikazu Saito Flux-free Finite Element Method with
Lagrange Multipliers for Two-fluid Flows 147--173
F. Lörcher and
G. Gassner and
C.-D. Munz A Discontinuous Galerkin Scheme Based on
a Space--Time Expansion. I. Inviscid
Compressible Flow in One Space Dimension 175--199
Bernardo Cockburn and
Ryuhei Ichikawa Adjoint Recovery of Superconvergent
Linear Functionals from Galerkin
Approximations. The One-dimensional Case 201--232
Bernardo Cockburn and
Bo Dong An Analysis of the Minimal Dissipation
Local Discontinuous Galerkin Method for
Convection--Diffusion Problems . . . . . 233--262
Jichun Li and
Aihua Wood Finite Element Analysis for Wave
Propagation in Double Negative
Metamaterials . . . . . . . . . . . . . 263--286
J. Martín-Vaquero and
J. Vigo-Aguiar Adapted BDF Algorithms: Higher-order
Methods and Their Stability . . . . . . 287--313
Tony F. Chan and
Hao-Min Zhou Total Variation Wavelet Thresholding . . 315--341
Y. Q. Huang and
Ruo Li and
Wenbin Liu Preconditioned Descent Algorithms for
$p$-Laplacian . . . . . . . . . . . . . 343--371
Bernard Bialecki and
Andreas Karageorghis A Nonoverlapping Domain Decomposition
Method for Legendre Spectral Collocation
Problems . . . . . . . . . . . . . . . . 373--409
G. Kitzhofer and
O. Koch and
P. Lima and
E. Weinmüller Efficient Numerical Solution of the
Density Profile Equation in
Hydrodynamics . . . . . . . . . . . . . 411--424
G. Kitzhofer and
O. Koch and
P. Lima and
E. Weinmüller Efficient Numerical Solution of the
Density Profile Equation in
Hydrodynamics . . . . . . . . . . . . . 425--425
Kelly Black and
John B. Geddes Complex Valued Spectral Hermite
Approximations for the Actively
Mode-Locked Laser . . . . . . . . . . . 427--448
James V. Lambers Practical Implementation of Krylov
Subspace Spectral Methods . . . . . . . 449--476
Ph. Ballereau and
M. Casanova and
F. Duboc and
D. Dureau Simulation of the Paraxial Laser
Propagation Coupled with Hydrodynamics
in $3$D Geometry . . . . . . . . . . . . 1--24
Barbara I. Wohlmuth An a Posteriori Error Estimator for
Two-Body Contact Problems on
Non-Matching Meshes . . . . . . . . . . 25--45
D. Sármány and
M. A. Botchev and
J. J. W. van der Vegt Dispersion and Dissipation Error in
High-Order Runge--Kutta Discontinuous
Galerkin Discretisations of the Maxwell
Equations . . . . . . . . . . . . . . . 47--74
Slimane Adjerid and
Mahboub Baccouch The Discontinuous Galerkin Method for
Two-Dimensional Hyperbolic Problems.
Part I: Superconvergence Error Analysis 75--113
Ke Chen and
Xue-Cheng Tai A Nonlinear Multigrid Method for Total
Variation Minimization from Image
Restoration . . . . . . . . . . . . . . 115--138
J. G. Verwer On Time Staggering for Wave Equations 139--154
Ruo Li and
Wenbin Liu and
Ningning Yan A Posteriori Error Estimates of Recovery
Type for Distributed Convex Optimal
Control Problems . . . . . . . . . . . . 155--182
E. Burman and
B. Stamm Minimal Stabilization for Discontinuous
Galerkin Finite Element Methods for
Hyperbolic Problems . . . . . . . . . . 183--208
Pavlo Kovalov and
Vadim Linetsky and
Michael Marcozzi Pricing Multi-Asset American Options: a
Finite Element Method-of-Lines with
Smooth Penalty . . . . . . . . . . . . . 209--237
Emil M. Constantinescu and
Adrian Sandu Multirate Timestepping Methods for
Hyperbolic Conservation Laws . . . . . . 239--278
Jun Shen and
Chi-Wang Shu and
Mengping Zhang A High Order WENO Scheme for a
Hierarchical Size-Structured Population
Model . . . . . . . . . . . . . . . . . 279--291
Giovanni Alessandrini and
Antonio Bilotta and
Antonino Morassi Computing Volume Bounds of Inclusions by
EIT Measurements . . . . . . . . . . . . 293--312
Ko-An Feng and
Chun-Hao Teng and
Min-Hung Chen A Pseudospectral Penalty Scheme for $2$D
Isotropic Elastic Wave Computations . . 313--348
Christos Arvanitis Mesh Redistribution Strategies and
Finite Element Schemes for Hyperbolic
Conservation Laws . . . . . . . . . . . 1--25
P.-E. Bernard and
E. Deleersnijder and
V. Legat and
J.-F. Remacle Dispersion Analysis of Discontinuous
Galerkin Schemes Applied to Poincaré,
Kelvin and Rossby Waves . . . . . . . . 26--47
Juan-Ming Yuan and
Jie Shen and
Jiahong Wu A Dual-Petrov--Galerkin Method for the
Kawahara-Type Equations . . . . . . . . 48--63
Guoxian Chen and
Huazhong Tang and
Pingwen Zhang Second-Order Accurate Godunov Scheme for
Multicomponent Flows on Moving
Triangular Meshes . . . . . . . . . . . 64--86
Hudong Chen and
Isaac Goldhirsch and
Steven A. Orszag Discrete Rotational Symmetry, Moment
Isotropy, and Higher Order Lattice
Boltzmann Models . . . . . . . . . . . . 87--112
Elsayed M. E. Elbarbary Efficient Chebyshev--Petrov--Galerkin
Method for Solving Second-Order
Equations . . . . . . . . . . . . . . . 113--126
Lars Ferm and
Per Lötstedt and
Andreas Hellander A Hierarchy of Approximations of the
Master Equation Scaled by a Size
Parameter . . . . . . . . . . . . . . . 127--151
Antony Jameson The Construction of Discretely
Conservative Finite Volume Schemes that
Also Globally Conserve Energy or Entropy 152--187
Antony Jameson Formulation of Kinetic Energy Preserving
Conservative Schemes for Gas Dynamics
and Direct Numerical Simulation of
One-Dimensional Viscous Compressible
Flow in a Shock Tube Using Entropy and
Kinetic Energy Preserving Schemes . . . 188--208
A. Almansa and
C. Ballester and
V. Caselles and
G. Haro A TV Based Restoration Model with Local
Constraints . . . . . . . . . . . . . . 209--236
Zhimin Zhang Superconvergence of a Chebyshev Spectral
Collocation Method . . . . . . . . . . . 237--246
Youngsoo Ha and
Carl L. Gardner Positive Scheme Numerical Simulation of
High Mach Number Astrophysical Jets . . 247--259
G. Gassner and
F. Lörcher and
C.-D. Munz A Discontinuous Galerkin Scheme based on
a Space--Time Expansion II. Viscous Flow
Equations in Multi Dimensions . . . . . 260--286
Michael D. Marcozzi On the Approximation of Infinite
Dimensional Optimal Stopping Problems
with Application to Mathematical Finance 287--307
D. Nordsletten and
N. P. Smith Triangulation of $p$-Order Parametric
Surfaces . . . . . . . . . . . . . . . . 308--335
Benjamin Berkels and
Andreas Rätz and
Martin Rumpf and
Axel Voigt Extracting Grain Boundaries and
Macroscopic Deformations from Images on
Atomic Scale . . . . . . . . . . . . . . 1--23
Thomas C. Cecil and
Stanley J. Osher and
Jianliang Qian Essentially Non-Oscillatory Adaptive
Tree Methods . . . . . . . . . . . . . . 25--41
P. A. Stewart and
N. Lay and
M. Sussman and
M. Ohta An Improved Sharp Interface Method for
Viscoelastic and Viscous Two-Phase Flows 43--61
Grzegorz Rz\kadkowski and
Slawomir Lepkowski A Generalization of the Euler--Maclaurin
Summation Formula: an Application to
Numerical Computation of the
Fermi--Dirac Integrals . . . . . . . . . 63--74
Stanley Osher Preface . . . . . . . . . . . . . . . . 75--76
Martin Burger and
Christina Stöcker and
Axel Voigt Finite Element--ased Level Set Methods
for Higher Order Flows . . . . . . . . . 77--98
Vicente F. Candela and
Antonio Marquina On the Numerical Approximation of the
Length of (Implicit) Level Curves . . . 99--113
Antoine du Chéné and
Chohong Min and
Frédéric Gibou Second-Order Accurate Computation of
Curvatures in a Level Set Framework
Using Novel High-Order Reinitialization
Schemes . . . . . . . . . . . . . . . . 114--131
Daniel Cremers Nonlinear Dynamical Shape Priors for
Level Set Segmentation . . . . . . . . . 132--143
Shi Jin and
Xu Yang Computation of the Semiclassical Limit
of the Schrödinger Equation with Phase
Shift by a Level Set Method . . . . . . 144--169
Chiu-Yen Kao and
Richard Tsai Properties of a Level Set Algorithm for
the Visibility Problems . . . . . . . . 170--191
Hailiang Liu and
Zhongming Wang Superposition of Multi-Valued Solutions
in High Frequency Wave Dynamics . . . . 192--218
Colin B. Macdonald and
Steven J. Ruuth Level Set Equations on Surfaces via the
Closest Point Method . . . . . . . . . . 219--240
Yan Xu and
Jaap J. W. van der Vegt and
Onno Bokhove Discontinuous Hamiltonian Finite Element
Method for Linear Hyperbolic Systems . . 241--265
Paul Macklin and
John S. Lowengrub A New Ghost Cell/Level Set Method for
Moving Boundary Problems: Application to
Tumor Growth . . . . . . . . . . . . . . 266--299
Ian M. Mitchell The Flexible, Extensible and Efficient
Toolbox of Level Set Methods . . . . . . 300--329
David Salac and
Wei Lu A Local Semi-Implicit Level-Set Method
for Interface Motion . . . . . . . . . . 330--349
Andrew Selle and
Ronald Fedkiw and
ByungMoon Kim and
Yingjie Liu An Unconditionally Stable MacCormack
Method . . . . . . . . . . . . . . . . . 350--371
Kensuke Yokoi A Numerical Method for Free-Surface
Flows and Its Application to Droplet
Impact on a Thin Liquid Layer . . . . . 372--396
Anne Gelb and
Dennis Cates Detection of Edges in Spectral Data
III--Refinement of the Concentration
Method . . . . . . . . . . . . . . . . . 1--43
T. G. Liu and
J. Y. Ho and
B. C. Khoo and
A. W. Chowdhury Numerical Simulation of Fluid-Structure
Interaction Using Modified Ghost Fluid
Method and Naviers Equations . . . . . . 45--68
Chin-Yun Chen Bivariate Product Cubature Using Peano
Kernels for Local Error Estimates . . . 69--88
Colin B. Macdonald and
Sigal Gottlieb and
Steven J. Ruuth A Numerical Study of Diagonally Split
Runge--Kutta Methods for PDEs with
Discontinuities . . . . . . . . . . . . 89--112
J. A. Carrillo and
T. Goudon and
P. Lafitte and
F. Vecil Numerical Schemes of Diffusion
Asymptotics and Moment Closures for
Kinetic Equations . . . . . . . . . . . 113--149
Bernardo Cockburn and
Haiying Wang The Computation of a Locally
Conservative Stress for the Continuous
Galerkin Method for Compressible
Linearly Elastic Materials . . . . . . . 151--163
Sébastien Loisel and
Reinhard Nabben and
Daniel B. Szyld On Hybrid Multigrid--Schwarz Algorithms 165--175
Zhiguang Xiong and
Yanping Chen A Rectangular Finite Volume Element
Method for a Semilinear Elliptic
Equation . . . . . . . . . . . . . . . . 177--191
E. D. Fernández-Nieto and
G. Narbona-Reina Extension of WAF Type Methods to
Non-Homogeneous Shallow Water Equations
with Pollutant . . . . . . . . . . . . . 193--217
Swapan K. Pandit On the Use of Compact
Streamfunction--Velocity Formulation of
Steady Navier--Stokes Equations on
Geometries beyond Rectangular . . . . . 219--242
Houde Han and
Zhongyi Huang and
R. Bruce Kellogg A Tailored Finite Point Method for a
Singular Perturbation Problem on an
Unbounded Domain . . . . . . . . . . . . 243--261
Rong Zhang and
Zhong-qing Wang and
Ben-yu Guo Mixed Fourier--Laguerre Spectral and
Pseudospectral Methods for Exterior
Problems Using Generalized Laguerre
Functions . . . . . . . . . . . . . . . 263--283
Hongxia Li and
Zhigang Wang and
De-kang Mao Numerically Neither Dissipative Nor
Compressive Scheme for Linear Advection
Equation and Its Application to the
Euler System . . . . . . . . . . . . . . 285--331
Adi Ditkowski and
Abhinav Bhandari and
Brian W. Sheldon Computing Derivatives of Noisy Signals
Using Orthogonal Functions Expansions 333--349
Chun-Hao Teng and
Bang-Yan Lin and
Hung-Chun Chang A Legendre Pseudospectral Penalty Scheme
for Solving Time-Domain Maxwell's
Equations . . . . . . . . . . . . . . . 351--390
Micol Pennacchio and
Valeria Simoncini Substructuring Preconditioners for
Mortar Discretization of a Degenerate
Evolution Problem . . . . . . . . . . . 391--419
Gerard Awanou Robustness of a Spline Element Method
with Constraints . . . . . . . . . . . . 421--432
Tim Schulze and
Vasilios Alexiades and
Xiaobing Feng Multi-scale Modeling and Simulation in
Materials Science, Preface . . . . . . . 1--2
Russel E. Caflisch Growth, Structure and Pattern Formation
for Thin Films . . . . . . . . . . . . . 3--17
Matthew Dobson and
Mitchell Luskin Iterative Solution of the Quasicontinuum
Equilibrium Equations with Continuation 19--41
Markos A. Katsoulakis and
Petr Plechác and
Luc Rey-Bellet Numerical and Statistical Methods for
the Coarse-Graining of Many-Particle
Stochastic Systems . . . . . . . . . . . 43--71
Chi-Hang Lam and
M. T. Lung and
Leonard M. Sander Fast Kinetic Monte Carlo Simulation of
Strained Heteroepitaxy in Three
Dimensions . . . . . . . . . . . . . . . 73--88
Lei Zhang and
Long-Qing Chen and
Qiang Du Mathematical and Numerical Aspects of a
Phase-field Approach to Critical Nuclei
Morphology in Solids . . . . . . . . . . 89--102
R. Glowinski and
T. Kärkkäinen and
T. Valkonen and
A. Ivannikov Non-smooth SOR for $ L^1 $-Fitting:
Convergence Study and Discussion of
Related Issues . . . . . . . . . . . . . 103--138
Thirupathi Gudi and
Neela Nataraj and
Amiya K. Pani Mixed Discontinuous Galerkin Finite
Element Method for the Biharmonic
Equation . . . . . . . . . . . . . . . . 139--161
Kris Van den Abeele and
Chris Lacor and
Z. J. Wang On the Stability and Accuracy of the
Spectral Difference Method . . . . . . . 162--188
Alina Chertock and
David Gottlieb and
Alex Solomonoff Modified Optimal Prediction and its
Application to a Particle-Method Problem 189--201
Lubomír Banas and
Robert Nürnberg Finite Element Approximation of a Three
Dimensional Phase Field Model for Void
Electromigration . . . . . . . . . . . . 202--232
Rosa Donat and
Pep Mulet Characteristic-Based Schemes for
Multi-Class Lighthill--Whitham--Richards
Traffic Models . . . . . . . . . . . . . 233--250
Haotao Cai An Efficient Algorithm for Solving the
Generalized Airfoil Equation . . . . . . 251--267
Adi Ditkowski Numerical Method for Solving
Discontinuous Initial/Final-Value
Problems . . . . . . . . . . . . . . . . 268--281
Jeremy Brandman A Level-Set Method for Computing the
Eigenvalues of Elliptic Operators
Defined on Compact Hypersurfaces . . . . 282--315
Lucia Parussini Fictitious Domain Approach Via Lagrange
Multipliers with Least Squares Spectral
Element Method . . . . . . . . . . . . . 316--335
Yves Achdou and
Frédéric Hecht and
David Pommier A Posteriori Error Estimates for
Parabolic Variational Inequalities . . . 336--366
Antonio Marquina and
Stanley J. Osher Image Super-Resolution by
TV-Regularization and Bregman Iteration 367--382
Hirofumi Notsu and
Masahisa Tabata A Single-Step Characteristic-Curve
Finite Element Scheme of Second Order in
Time for the Incompressible
Navier--Stokes Equations . . . . . . . . 1--14
Slimane Adjerid and
Mahboub Baccouch The Discontinuous Galerkin Method for
Two-dimensional Hyperbolic Problems.
Part II: a Posteriori Error Estimation 15--49
Ruben Juanes and
Sébastien F. Matringe Unified Formulation for High-Order
Streamline Tracing on Two-Dimensional
Unstructured Grids . . . . . . . . . . . 50--73
Xiaobing Feng and
Michael Neilan Vanishing Moment Method and Moment
Solutions for Fully Nonlinear Second
Order Partial Differential Equations . . 74--98
Paolo Zunino Discontinuous Galerkin Methods Based on
Weighted Interior Penalties for Second
Order PDEs with Non-smooth Coefficients 99--126
Qiang Zhang and
Zi-Long Wu Numerical Simulation for Porous Medium
Equation by Local Discontinuous Galerkin
Finite Element Method . . . . . . . . . 127--148
Hanquan Wang Numerical Simulations on Stationary
States for Rotating Two-Component
Bose--Einstein Condensates . . . . . . . 149--163
David Walfisch and
Jennifer K. Ryan and
Robert M. Kirby One-Sided Smoothness-Increasing
Accuracy-Conserving Filtering for
Enhanced Streamline Integration through
Discontinuous Fields . . . . . . . . . . 164--184
Qi Zhu and
Ying Qiao and
Shaohua Tan A Robust High-Order Mixed $ L_2 $--$
L_\infty $ Estimation for
Linear-in-the-Parameters Models . . . . 185--206
Chokri Chniti and
Frédéric Nataf and
Francis Nier Improved Interface Conditions for 2 $D$
Domain Decomposition with Corners:
Numerical Applications . . . . . . . . . 207--228
Adrian Sandu and
Emil M. Constantinescu Multirate Explicit Adams Methods for
Time Integration of Conservation Laws 229--249
Sigal Gottlieb and
David I. Ketcheson and
Chi-Wang Shu High Order Strong Stability Preserving
Time Discretizations . . . . . . . . . . 251--289
Hongfei Fu and
Hongxing Rui A Priori Error Estimates for Optimal
Control Problems Governed by Transient
Advection--Diffusion Equations . . . . . 290--315
Per-Gunnar Martinsson A Fast Direct Solver for a Class of
Elliptic Partial Differential Equations 316--330
Florentina Tone On the Long-Time $ H^2 $-Stability of
the Implicit Euler Scheme for the $2$D
Magnetohydrodynamics Equations . . . . . 331--348
Axel Klar and
Philip Reuterswärd and
Mohammed Sea\"\id A Semi-Lagrangian Method for a
Fokker--Planck Equation Describing Fiber
Dynamics . . . . . . . . . . . . . . . . 349--367
Andreas Glaser and
Vladimir Rokhlin A New Class of Highly Accurate Solvers
for Ordinary Differential Equations . . 368--399
Daniel C. Cole and
Yi Zou Subharmonic Resonance Behavior for the
Classical Hydrogen Atomic System . . . . 1--27
Tormod Bjòntegaard and
Yvon Maday and
Einar M. Rònquist Fast Tensor-Product Solvers: Partially
Deformed Three-dimensional Domains . . . 28--48
Jae-Hun Jung A Note on the Spectral Collocation
Approximation of Some Differential
Equations with Singular Source Terms . . 49--66
M. J. Castro and
E. D. Fernández-Nieto and
A. M. Ferreiro High Order Extensions of Roe Schemes for
Two-Dimensional Nonconservative
Hyperbolic Systems . . . . . . . . . . . 67--114
Inmaculada Higueras Characterizing Strong Stability
Preserving Additive Runge--Kutta Methods 115--128
Jinjie Liu and
Moysey Brio and
Jerome V. Moloney Overlapping Yee FDTD Method on
Nonorthogonal Grids . . . . . . . . . . 129--143
Isaac Dooley and
Sandhya Mangala and
Laxmikant Kale Parallel Simulations of Dynamic Fracture
Using Extrinsic Cohesive Elements . . . 144--165
Christophe Vandekerckhove and
Ioannis Kevrekidis An Efficient Newton--Krylov
Implementation of the Constrained Runs
Scheme for Initializing on a Slow
Manifold . . . . . . . . . . . . . . . . 167--188
Emiliano Cristiani A Fast Marching Method for
Hamilton--Jacobi Equations Modeling
Monotone Front Propagations . . . . . . 189--205
Yanping Chen and
Yongquan Dai Superconvergence for Optimal Control
Problems Governed by Semi-linear
Elliptic Equations . . . . . . . . . . . 206--221
Wuming Zhu and
David A. Kopriva A Spectral Element Method to Price
European Options. I. Single Asset with
and without Jump Diffusion . . . . . . . 222--243
Rodrigo B. Platte and
Anne Gelb A Hybrid Fourier--Chebyshev Method for
Partial Differential Equations . . . . . 244--264
Tommy L. Binford, Jr. and
David P. Nicholls and
Nilima Nigam Exact Non-Reflecting Boundary Conditions
on Perturbed Domains and $ h p $-Finite
Elements . . . . . . . . . . . . . . . . 265--292
Jun Zhu and
Jianxian Qiu Hermite WENO Schemes and Their
Application as Limiters for Runge--Kutta
Discontinuous Galerkin Method, III:
Unstructured Meshes . . . . . . . . . . 293--321
Wuming Zhu and
David A. Kopriva A Spectral Element Approximation to
Price European Options. II. The
Black--Scholes Model with Two Underlying
Assets . . . . . . . . . . . . . . . . . 323--339
J. M. Tang and
R. Nabben and
C. Vuik and
Y. A. Erlangga Comparison of Two-Level Preconditioners
Derived from Deflation, Domain
Decomposition and Multigrid Methods . . 340--370
Mofdi El-Amrani and
Mohammed Sea\"\id A Spectral Stochastic Semi-Lagrangian
Method for Convection--Diffusion
Equations with Uncertainty . . . . . . . 371--393
Adi Ditkowski and
Yuval Harness High-Order Embedded Finite Difference
Schemes for Initial Boundary Value
Problems on Time Dependent Irregular
Domains . . . . . . . . . . . . . . . . 394--440
Yana Di and
Ruo Li Computation of Dendritic Growth with
Level Set Model Using a Multi-Mesh
Adaptive Finite Element Method . . . . . 441--453
Magnus Svärd and
Siddhartha Mishra Shock Capturing Artificial Dissipation
for High-Order Finite Difference Schemes 454--484
Bernardo Cockburn and
Chi-Wang Shu Foreword . . . . . . . . . . . . . . . . 1--3
Blanca Ayuso de Dios and
Ludmil Zikatanov Uniformly Convergent Iterative Methods
for Discontinuous Galerkin
Discretizations . . . . . . . . . . . . 4--36
Susanne C. Brenner and
Thirupathi Gudi and
Li-yeng Sung A Posteriori Error Control for a Weakly
Over-Penalized Symmetric Interior
Penalty Method . . . . . . . . . . . . . 37--50
Susanne C. Brenner and
Fengyan Li and
Li-yeng Sung Nonconforming Maxwell Eigensolvers . . . 51--85
Annalisa Buffa and
Ilaria Perugia and
Tim Warburton The Mortar-Discontinuous Galerkin Method
for the $2$D Maxwell Eigenproblem . . . 86--114
Ayçil Çesmelioglu and
Béatrice Rivi\`ere Primal Discontinuous Galerkin Methods
for Time-Dependent Coupled Surface and
Subsurface Flow . . . . . . . . . . . . 115--140
Bernardo Cockburn and
Bo Dong and
Johnny Guzmán A Hybridizable and Superconvergent
Discontinuous Galerkin Method for
Biharmonic Problems . . . . . . . . . . 141--187
Bernardo Cockburn and
Guido Kanschat and
Dominik Schötzau An Equal-Order DG Method for the
Incompressible Navier--Stokes Equations 188--210
Yekaterina Epshteyn and
Ahmet Izmirlioglu Fully Discrete Analysis of a
Discontinuous Finite Element Method for
the Keller--Segel Chemotaxis Model . . . 211--256
Marcus J. Grote and
Dominik Schötzau Optimal Error Estimates for the Fully
Discrete Interior Penalty DG Method for
the Wave Equation . . . . . . . . . . . 257--272
Johnny Guzmán and
Béatrice Rivi\`ere Sub-optimal Convergence of Non-symmetric
Discontinuous Galerkin Methods for Odd
Polynomial Approximations . . . . . . . 273--280
Paul Houston and
Dominik Schötzau and
Xiaoxi Wei A Mixed DG Method for Linearized
Incompressible Magnetohydrodynamics . . 281--314
Ethan J. Kubatko and
Shintaro Bunya and
Clint Dawson A Performance Comparison of Continuous
and Discontinuous Finite Element Shallow
Water Models . . . . . . . . . . . . . . 315--339
Carlo Lovadina and
L. Donatella Marini A-Posteriori Error Estimates for
Discontinuous Galerkin Approximations of
Second Order Elliptic Problems . . . . . 340--359
Wei Wang and
Chi-Wang Shu The WKB Local Discontinuous Galerkin
Method for the Simulation of Schrödinger
Equation in a Resonant Tunneling Diode 360--374
Yan Xu and
Chi-Wang Shu Local Discontinuous Galerkin Method for
Surface Diffusion and Willmore Flow of
Graphs . . . . . . . . . . . . . . . . . 375--390
Jianfeng Zhu and
Yong-Tao Zhang and
Stuart A. Newman Application of Discontinuous Galerkin
Methods for Reaction--Diffusion Systems
in Developmental Biology . . . . . . . . 391--418
S. Abarbanel and
H. Qasimov and
S. Tsynkov Long-Time Performance of Unsplit PMLs
with Explicit Second Order Schemes . . . 1--12
Chang-Yeol Jung Evolution of Probability Distribution in
Time for Solutions of Hyperbolic
Equations . . . . . . . . . . . . . . . 13--48
Scott A. Sarra Edge Detection Free Postprocessing for
Pseudospectral Approximations . . . . . 49--61
J. Hughes and
M. Friedman A Bisection-Like Algorithm for Branch
Switching at a Simple Branch Point . . . 62--69
Zuozheng Zhang and
Ziqing Xie and
Zhimin Zhang Superconvergence of Discontinuous
Galerkin Methods for
Convection--Diffusion Problems . . . . . 70--93
Marco Kupiainen and
Björn Sjögreen A Cartesian Embedded Boundary Method for
the Compressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 94--117
Arunasalam Rahunanthan and
Dan Stanescu Stable Interface Conditions for
Discontinuous Galerkin Approximations of
Navier--Stokes Equations . . . . . . . . 118--138
Elena Celledoni and
Bawfeh Kingsley Kometa Semi-Lagrangian Runge--Kutta Exponential
Integrators for Convection Dominated
Problems . . . . . . . . . . . . . . . . 139--164
R. Kannan and
Z. J. Wang A Study of Viscous Flux Formulations for
a $ f p$-Multigrid Spectral Volume
Navier--Stokes Solver . . . . . . . . . 165--199
Houde Han and
Zhongyi Huang Tailored Finite Point Method for a
Singular Perturbation Problem with
Variable Coefficients in Two Dimensions 200--220
Stephanie Delage-Santacreu and
Stephane Vincent Tracking Fronts in One and Two-phase
Incompressible Flows Using an Adaptive
Mesh Refinement Approach . . . . . . . . 221--237
Liang Ge and
Wenbin Liu and
Danping Yang Adaptive Finite Element Approximation
for a Constrained Optimal Control
Problem via Multi-meshes . . . . . . . . 238--255
Zhongying Chen and
Gnaneshwar Nelakanti and
Yuesheng Xu A Fast Collocation Method for
Eigen-Problems of Weakly Singular
Integral Operators . . . . . . . . . . . 256--272
Ningning Yan and
Zhaojie Zhou A RT Mixed FEM/DG Scheme for Optimal
Control Governed by Convection Diffusion
Equations . . . . . . . . . . . . . . . 273--299
Yen Ting Ng and
Han Chen and
Chohong Min and
Frédéric Gibou Guidelines for Poisson Solvers on
Irregular Domains with Dirichlet
Boundary Conditions Using the Ghost
Fluid Method . . . . . . . . . . . . . . 300--320
Yunqing Huang and
Jichun Li Interior Penalty Discontinuous Galerkin
Method for Maxwell's Equations in Cold
Plasma . . . . . . . . . . . . . . . . . 321--340
R. Belaouar and
N. Crouseilles and
P. Degond and
E. Sonnendrücker An Asymptotically Stable Semi-Lagrangian
scheme in the Quasi-neutral Limit . . . 341--365
Ken Mattsson and
Frank Ham and
Gianluca Iaccarino Stable Boundary Treatment for the Wave
Equation on Second-Order Form . . . . . 366--383
Chang-Yeol Jung and
Roger Temam Finite Volume Approximation of
One-Dimensional Stiff
Convection--Diffusion Equations . . . . 384--410
Ming Xiang and
Shaozhong Deng and
Wei Cai A Sixth-order Image Approximation to the
Ionic Solvent Induced Reaction Field . . 411--435
Fuzheng Gao and
Jianxian Qiu and
Qiang Zhang Local Discontinuous Galerkin Finite
Element Method and Error Estimates for
One Class of Sobolev Equation . . . . . 436--460
Li-ping He Error Estimation of a Class of Stable
Spectral Approximation to the
Cahn--Hilliard Equation . . . . . . . . 461--482
F. Bouchut and
T. Morales de Luna Semi-discrete Entropy Satisfying
Approximate Riemann Solvers. The Case of
the Suliciu Relaxation Approximation . . 483--509
Qingqu Zhuang and
Jie Shen and
Chuanju Xu A Coupled Legendre--Laguerre
Spectral-Element Method for the
Navier--Stokes Equations in Unbounded
Domains . . . . . . . . . . . . . . . . 1--22
Marcos Pimenta de Abreu On the Dependence of Discrete Ordinates
Models for Layer Reflectance and
Transmittance on Relative Optical Depth
and Solar Zenith Angle . . . . . . . . . 23--37
Sheng-Long Hu and
Zheng-Hai Huang and
Nan Lu A Non-monotone Line Search Algorithm for
Unconstrained Optimization . . . . . . . 38--53
Emmanuil H. Georgoulis and
Edward Hall and
Jens Markus Melenk On the Suboptimality of the $p$-Version
Interior Penalty Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 54--67
Evgeniy Romenski and
Dimitris Drikakis and
Eleuterio Toro Conservative Models and Numerical
Methods for Compressible Two-Phase Flow 68--95
Adrian Sescu and
Abdollah A. Afjeh and
Ray Hixon and
Carmen Sescu Conditionally Stable Multidimensional
Schemes for Advective Equations . . . . 96--117
S. C. Brenner and
T. Gudi and
L. Owens and
L.-Y. Sung An Intrinsically Parallel Finite Element
Method . . . . . . . . . . . . . . . . . 118--121
Vít Dolejsí and
Oto Havle The $ L^2 $-Optimality of the IIPG
Method for Odd Degrees of Polynomial
Approximation in $1$D . . . . . . . . . 122--143
Bernardo Cockburn and
Deepa Gupta and
Fernando Reitich Boundary-Conforming Discontinuous
Galerkin Methods via Extensions from
Subdomains . . . . . . . . . . . . . . . 144--184
Yifei Lou and
Xiaoqun Zhang and
Stanley Osher and
Andrea Bertozzi Image Recovery via Nonlocal Operators 185--197
Ting-Ting Shen and
Zhong-Qiang Zhang and
He-Ping Ma Optimal Error Estimates of the Legendre
Tau Method for Second-Order Differential
Equations . . . . . . . . . . . . . . . 198--215
M. Ben-Artzi and
J.-P. Croisille and
D. Fishelov A High Order Compact Scheme for the
Pure-Streamfunction Formulation of the
Navier--Stokes Equations . . . . . . . . 216--250
O. Bokanowski and
E. Cristiani and
H. Zidani An Efficient Data Structure and Accurate
Scheme to Solve Front Propagation
Problems . . . . . . . . . . . . . . . . 251--273
Maria Kakleas and
David P. Nicholls Numerical Simulation of a Weakly
Nonlinear Model for Water Waves with
Viscosity . . . . . . . . . . . . . . . 274--290
Zhong-Qing Wang and
Li-Lian Wang A Collocation Method with Exact
Imposition of Mixed Boundary Conditions 291--317
Xin Wen A High Order Numerical Method for
Computing Physical Observables in the
Semiclassical Limit of the
One-Dimensional Linear Schrödinger
Equation with Discontinuous Potentials 318--344
Morgane Bergot and
Gary Cohen and
Marc Duruflé Higher-order Finite Elements for Hybrid
Meshes Using New Nodal Pyramidal
Elements . . . . . . . . . . . . . . . . 345--381
Yanping Chen and
Yunqing Huang and
Wenbin Liu and
Ningning Yan Error Estimates and Superconvergence of
Mixed Finite Element Methods for Convex
Optimal Control Problems . . . . . . . . 382--403
H. Yousefi and
A. Noorzad and
J. Farjoodi Simulating $2$D Waves Propagation in
Elastic Solid Media Using Wavelet Based
Adaptive Method . . . . . . . . . . . . 404--425
Wuming Zhu and
David A. Kopriva A Spectral Element Approximation to
Price European Options with One Asset
and Stochastic Volatility . . . . . . . 426--446
Othmar Koch and
Christopher Ede and
Gerald Jordan Hierarchical Matrices in Computations of
Electron Dynamics . . . . . . . . . . . 447--455
Sergio Amat and
Juan Ruiz and
J. Carlos Trillo Fast Multiresolution Algorithms and
Their Related Variational Problems for
Image Denoising . . . . . . . . . . . . 1--23
Pengtao Sun and
Long Chen and
Jinchao Xu Numerical Studies of Adaptive Finite
Element Methods for Two Dimensional
Convection-Dominated Problems . . . . . 24--43
K. van den Doel and
U. M. Ascher and
A. Leitão Multiple Level Sets for Piecewise
Constant Surface Reconstruction in
Highly Ill-Posed Problems . . . . . . . 44--66
Lino J. Alvarez-Vázquez and
Francisco J. Fernández Optimal Management of a Bioreactor for
Eutrophicated Water Treatment: a
Numerical Approach . . . . . . . . . . . 67--91
G. Lin and
A. M. Tartakovsky Numerical Studies of Three-dimensional
Stochastic Darcy's Equation and
Stochastic
Advection--Diffusion-Dispersion Equation 92--117
Daniel J. Bodony Accuracy of the
Simultaneous-Approximation-Term Boundary
Condition for Time-Dependent Problems 118--133
Juan A. Acebrón and
Ángel Rodríguez-Rozas and
Renato Spigler Efficient Parallel Solution of Nonlinear
Parabolic Partial Differential Equations
by a Probabilistic Domain Decomposition 135--157
F. Ar\`andiga and
A. M. Belda and
P. Mulet Point-Value WENO Multiresolution
Applications to Stable Image Compression 158--182
M. Afif and
B. Amaziane and
G. Kunert and
Z. Mghazli and
S. Nicaise A Posteriori Error Estimation for a
Finite Volume Discretization on
Anisotropic Meshes . . . . . . . . . . . 183--200
Ben-Yu Guo and
Yong-Gang Yi Generalized Jacobi Rational Spectral
Method and Its Applications . . . . . . 201--238
Yintzer Shih and
R. Bruce Kellogg and
Peishan Tsai A Tailored Finite Point Method for
Convection--Diffusion-Reaction Problems 239--260
Raimund Bürger and
Ricardo Ruiz-Baier and
Kai Schneider Adaptive Multiresolution Methods for the
Simulation of Waves in Excitable Media 261--290
Olivier Pironneau and
Alfio Quarteroni and
Masahisa Tabata Preface . . . . . . . . . . . . . . . . 291--292
Erik Burman and
Alfio Quarteroni and
Benjamin Stamm Interior Penalty Continuous and
Discontinuous Finite Element
Approximations of Hyperbolic Equations 293--312
M. Flueck and
A. Janka and
C. Laurent and
M. Picasso and
J. Rappaz Some Mathematical and Numerical Aspects
in Aluminum Production . . . . . . . . . 313--325
Sashikumaar Ganesan and
Lutz Tobiska Stabilization by Local Projection for
Convection--Diffusion and Incompressible
Flow Problems . . . . . . . . . . . . . 326--342
Thomas J. R. Hughes and
Guglielmo Scovazzi Stabilized Methods for Compressible
Flows . . . . . . . . . . . . . . . . . 343--368
Hyung-Chun Lee and
Guang-Ri Piao Boundary Feedback Control of the Burgers
Equations by a Reduced-Order Approach
Using Centroidal Voronoi Tessellations 369--387
Mitsuhiro T. Nakao and
Yoshitaka Watanabe and
Nobito Yamamoto Computer Assisted Proofs of Bifurcating
Solutions for Nonlinear Heat Convection
Problems . . . . . . . . . . . . . . . . 388--401
Olivier Pironneau Finite Element Characteristic Methods
Requiring no Quadrature . . . . . . . . 402--415
Hongxing Rui and
Masahisa Tabata A Mass-Conservative Characteristic
Finite Element Scheme for
Convection--Diffusion Problems . . . . . 416--432
Yuzuru Eguchi Development of a Variational Multiscale
Large-Eddy Simulation Code `MISTRAL'
Using Double-Scale Finite Elements . . . 433--453
Petr Knobloch Numerical Solution of
Convection--Diffusion Equations Using a
Nonlinear Method of Upwind Type . . . . 454--470
Hidenori Yasuda Two-Phase Shallow Water Equations and
Phase Separation in Thin Immiscible
Liquid Films . . . . . . . . . . . . . . 471--487
Fatih Celiker and
Bernardo Cockburn and
Ke Shi Hybridizable Discontinuous Galerkin
Methods for Timoshenko Beams . . . . . . 1--37
S. M. Wise Unconditionally Stable Finite
Difference, Nonlinear Multigrid
Simulation of the
Cahn--Hilliard--Hele--Shaw System of
Equations . . . . . . . . . . . . . . . 38--68
Hongtao Yang A Numerical Analysis of American Options
with Regime Switching . . . . . . . . . 69--91
Yinnian He and
Liquan Mei and
Yueqiang Shang and
Juan Cui Newton Iterative Parallel Finite Element
Algorithm for the Steady Navier--Stokes
Equations . . . . . . . . . . . . . . . 92--106
Mitsuhiro T. Nakao and
Yoshitaka Watanabe and
Nobito Yamamoto Erratum to: Computer Assisted Proofs of
Bifurcating Solutions for Nonlinear Heat
Convection Problems . . . . . . . . . . 107--107
Yintzer Shih and
R. Bruce Kellogg and
Peishan Tsai Erratum to: A Tailored Finite Point
Method for
Convection--Diffusion-Reaction Problems 108--108
V. A. Dougalis and
D. E. Mitsotakis and
J.-C. Saut Boussinesq Systems of Bona--Smith Type
on Plane Domains: Theory and Numerical
Analysis . . . . . . . . . . . . . . . . 109--135
David A. Kopriva and
Gregor Gassner On the Quadrature and Weak Form Choices
in Collocation Type Discontinuous
Galerkin Spectral Element Methods . . . 136--155
J. Guzmán A Unified Analysis of Several Mixed
Methods for Elasticity with Weak Stress
Symmetry . . . . . . . . . . . . . . . . 156--169
Antoine Bourgeade and
Candice Mézel and
Olivier Saut Modeling the Early Ionization of
Dielectrics by Ultrashort Laser Pulses 170--190
D. Conte and
R. D'Ambrosio and
Z. Jackiewicz Two-step Runge--Kutta Methods with
Quadratic Stability Functions . . . . . 191--218
D. Sármány and
F. Izsák and
J. J. W. van der Vegt Optimal Penalty Parameters for Symmetric
Discontinuous Galerkin Discretisations
of the Time-Harmonic Maxwell Equations 219--254
Ben-Yu Guo and
Tian-Jun Wang Composite Laguerre--Legendre Spectral
Method for Fourth-Order Exterior
Problems . . . . . . . . . . . . . . . . 255--285
Alfa R. H. Heryudono and
Tobin A. Driscoll Radial Basis Function Interpolation on
Irregular Domain through Conformal
Transplantation . . . . . . . . . . . . 286--300
Yunqing Huang and
Nianyu Yi The Superconvergent Cluster Recovery
Method . . . . . . . . . . . . . . . . . 301--322
Haiyang Gao and
Z. J. Wang and
Yen Liu A Study of Curved Boundary
Representations for $2$D High Order
Euler Solvers . . . . . . . . . . . . . 323--336
Sigal Gottlieb and
Chi-Wang Shu Foreword . . . . . . . . . . . . . . . . 1--2
R. Abgrall and
J. Trefilík An Example of High Order Residual
Distribution Scheme Using non-Lagrange
Elements . . . . . . . . . . . . . . . . 3--25
S. Britt and
S. Tsynkov and
E. Turkel A Compact Fourth Order Scheme for the
Helmholtz Equation in Polar Coordinates 26--47
Jed Brown Efficient Nonlinear Solvers for Nodal
High-Order Finite Elements in $3$D . . . 48--63
Alexandre Caboussat and
Roland Glowinski Numerical Methods for the Vector-Valued
Solutions of Non-smooth Eigenvalue
Problems . . . . . . . . . . . . . . . . 64--89
Eric Canc\`es and
Rachida Chakir and
Yvon Maday Numerical Analysis of Nonlinear
Eigenvalue Problems . . . . . . . . . . 90--117
Mark H. Carpenter and
Jan Nordström and
David Gottlieb Revisiting and Extending Interface
Penalties for Multi-domain
Summation-by-Parts Operators . . . . . . 118--150
M. Catral and
S. J. Kirkland and
M. Neumann and
N.-S. Sze The Kemeny Constant for Finite
Homogeneous Ergodic Markov Chains . . . 151--166
Qingshan Chen and
Ming-Cheng Shiue and
Roger Temam The Barotropic Mode for the Primitive
Equations . . . . . . . . . . . . . . . 167--199
Alina Chertock and
Charles R. Doering and
Eugene Kashdan A Fast Explicit Operator Splitting
Method for Passive Scalar Advection . . 200--214
B. Cockburn and
N. C. Nguyen and
J. Peraire A Comparison of HDG Methods for Stokes
Flow . . . . . . . . . . . . . . . . . . 215--237
D. Fishelov and
M. Ben-Artzi and
J.-P. Croisille Recent Developments in the Pure
Streamfunction Formulation of the
Navier--Stokes System . . . . . . . . . 238--258
Daniele Funaro Numerical Simulation of Electromagnetic
Solitons and Their Interaction with
Matter . . . . . . . . . . . . . . . . . 259--271
Tom Goldstein and
Xavier Bresson and
Stanley Osher Geometric Applications of the Split
Bregman Method: Segmentation and Surface
Reconstruction . . . . . . . . . . . . . 272--293
Max Gunzburger and
Eunjung Lee and
Yuki Saka and
Catalin Trenchea Analysis of Nonlinear Spectral
Eddy--Viscosity Models of Turbulence . . 294--332
A. Ilyevsky and
E. Turkel Stopping Criteria for Anisotropic PDEs
in Image Processing . . . . . . . . . . 333--347
Antony Jameson A Proof of the Stability of the Spectral
Difference Method for All Orders of
Accuracy . . . . . . . . . . . . . . . . 348--358
Jae-Hun Jung and
Sigal Gottlieb and
Saeja Oh Kim Recovery of High Order Accuracy in
Radial Basis Function Approximations of
Discontinuous Problems . . . . . . . . . 359--381
Smadar Karni and
Gerardo Hernández-Dueñas A Hybrid Algorithm for the
Baer--Nunziato Model Using the Riemann
Invariants . . . . . . . . . . . . . . . 382--403
Fengyan Li and
Sergey Yakovlev A Central Discontinuous Galerkin Method
for Hamilton--Jacobi Equations . . . . . 404--428
Bang-Yan Lin and
Chun-Hao Teng and
Hung-Chun Chang Pseudospectral Modeling of Nano-Optics
in Ag Sphere Arrays . . . . . . . . . . 429--446
Hanieh Mirzaee and
Jennifer K. Ryan and
Robert M. Kirby Quantification of Errors Introduced in
the Numerical Approximation and
Implementation of Smoothness-Increasing
Accuracy Conserving (SIAC) Filtering of
Discontinuous Galerkin (DG) Fields . . . 447--470
David P. Nicholls and
Joseph Orville A Boundary Perturbation Method for
Vector Electromagnetic Scattering from
Families of Doubly Periodic Gratings . . 471--486
Adityavikram Viswanathan and
Anne Gelb and
Douglas Cochran On Reconstruction from Non-uniform
Spectral Data . . . . . . . . . . . . . 487--513
Tao Xiong and
Mengping Zhang and
Yong-Tao Zhang and
Chi-Wang Shu Fast Sweeping Fifth Order WENO Scheme
for Static Hamilton--Jacobi Equations
with Accurate Boundary Treatment . . . . 514--536
Zhonghua Qiao and
Changhui Yao and
Shanghui Jia Superconvergence and Extrapolation
Analysis of a Nonconforming Mixed Finite
Element Approximation for Time-Harmonic
Maxwell's Equations . . . . . . . . . . 1--19
Xiaoqun Zhang and
Martin Burger and
Stanley Osher A Unified Primal--Dual Algorithm
Framework Based on Bregman Iteration . . 20--46
J. H. M. ten Thije Boonkkamp and
M. J. H. Anthonissen The Finite Volume-Complete Flux Scheme
for Advection--Diffusion-Reaction
Equations . . . . . . . . . . . . . . . 47--70
Amiya K. Pani and
Sangita Yadav An $ h p $-local Discontinuous Galerkin
Method for Parabolic
Integro--Differential Equations . . . . 71--99
Christian Vergara Nitsche's Method for Defective Boundary
Value Problems in Incompressibile
Fluid-dynamics . . . . . . . . . . . . . 100--123
Paola F. Antonietti and
Paul Houston A Class of Domain Decomposition
Preconditioners for $ h p
$-Discontinuous Galerkin Finite Element
Methods . . . . . . . . . . . . . . . . 124--149
Thomas P. Wihler and
Béatrice Rivi\`ere Discontinuous Galerkin Methods for
Second-Order Elliptic PDE with
Low-Regularity Solutions . . . . . . . . 151--165
Kensuke Yokoi Numerical Method for Interaction Among
Multi-particle, Fluid and Arbitrary
Shape Structure . . . . . . . . . . . . 166--181
Wei Gong and
Ningning Yan A Mixed Finite Element Scheme for
Optimal Control Problems with Pointwise
State Constraints . . . . . . . . . . . 182--203
Francis Filbet and
Shi Jin An Asymptotic Preserving Scheme for the
ES--BGK Model of the Boltzmann Equation 204--224
Jae-Hun Jung and
Wolfgang Stefan A Simple Regularization of the
Polynomial Interpolation for the
Resolution of the Runge Phenomenon . . . 225--242
Wladimir J. van der Laan and
Andrei C. Jalba A Memory and Computation Efficient
Sparse Level-Set Method . . . . . . . . 243--264
Rajendra K. Ray A Transformation-free HOC Scheme for
Incompressible Viscous Flow Past a
Rotating and Translating Circular
Cylinder . . . . . . . . . . . . . . . . 265--293
Qiang Zhang Third Order Explicit Runge--Kutta
Discontinuous Galerkin Method for Linear
Conservation Law with Inflow Boundary
Condition . . . . . . . . . . . . . . . 294--313
R. Kannan and
Z. J. Wang LDG2: a Variant of the LDG Flux
Formulation for the Spectral Volume
Method . . . . . . . . . . . . . . . . . 314--328
S. Tanaka and
S. Bunya and
J. J. Westerink and
C. Dawson Scalability of an Unstructured Grid
Continuous Galerkin Based Hurricane
Storm Surge Model . . . . . . . . . . . 329--358
Fei Teng and
Li Yuan and
Tao Tang A Speed-Up Strategy for Finite Volume
WENO Schemes for Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 359--378
Bishnu P. Lamichhane A Mixed Finite Element Method for the
Biharmonic Problem Using Biorthogonal or
Quasi-Biorthogonal Systems . . . . . . . 379--396
Martin Vohralík Guaranteed and Fully Robust a posteriori
Error Estimates for Conforming
Discretizations of Diffusion Problems
with Discontinuous Coefficients . . . . 397--438
Suniti Karunatillake and
Steven W. Squyres Recipes for Spatial Statistics with
Global Datasets: a Martian Case Study 439--451
Tchavdar T. Marinov and
Keng Deng Characteristic Line Based Schemes for
Solving a Quasilinear Hierarchical
Size-Structured Model . . . . . . . . . 452--469
Huimin Wang and
Guangwu Yan and
Bo Yan Lattice Boltzmann Model Based on the
Rebuilding-Divergency Method for the
Laplace Equation and the Poisson
Equation . . . . . . . . . . . . . . . . 470--484
Bernardo Llanas and
Sagrario Lantarón Edge Detection by Adaptive Splitting . . 485--518
A. Karageorghis Efficient MFS Algorithms for
Inhomogeneous Polyharmonic Problems . . 519--541
Jichun Li Unified Analysis of Leap-Frog Methods
for Solving Time-Domain Maxwell's
Equations in Dispersive Media . . . . . 1--26
A. T. Barker and
S. C. Brenner and
E.-H. Park and
L.-Y. Sung Two-Level Additive Schwarz
Preconditioners for a Weakly
Over-Penalized Symmetric Interior
Penalty Method . . . . . . . . . . . . . 27--49
P. E. Vincent and
P. Castonguay and
A. Jameson A New Class of High-Order Energy Stable
Flux Reconstruction Schemes . . . . . . 50--72
Jing Zhang and
Li-Lian Wang and
Zhijian Rong A Prolate-Element Method for Nonlinear
PDEs on the Sphere . . . . . . . . . . . 73--92
Shao-Chun Chen and
Ya-Na Wang Conforming Rectangular Mixed Finite
Elements for Elasticity . . . . . . . . 93--108
S. L. Yilmaz and
M. B. Nik and
M. R. H. Sheikhi and
P. A. Strakey An Irregularly Portioned Lagrangian
Monte Carlo Method for Turbulent Flow
Simulation . . . . . . . . . . . . . . . 109--125
Mohammad Motamed and
Colin B. Macdonald and
Steven J. Ruuth On the Linear Stability of the
Fifth-Order WENO Discretization . . . . 127--149
Rongsan Chen and
De-kang Mao Entropy-TVD Scheme for Nonlinear Scalar
Conservation Laws . . . . . . . . . . . 150--169
Arnab Chaudhuri and
Abdellah Hadjadj and
Ashwin Chinnayya Numerical Study of Compressible Mixing
Layers Using High-Order WENO Schemes . . 170--197
Yintzer Shih and
R. Bruce Kellogg and
Yoyo Chang Characteristic Tailored Finite Point
Method for Convection-Dominated
Convection--Diffusion-Reaction Problems 198--215
Shuhai Zhang and
Shufen Jiang and
Chi-Wang Shu Improvement of Convergence to Steady
State Solutions of Euler Equations with
the WENO Schemes . . . . . . . . . . . . 216--238
Wei Guo and
Fengyan Li and
Jianxian Qiu Local-Structure-Preserving Discontinuous
Galerkin Methods with Lax--Wendroff Type
Time Discretizations for
Hamilton--Jacobi Equations . . . . . . . 239--257
Haijian Yang and
Xiao-Chuan Cai Parallel Two-Grid Semismooth
Newton--Krylov--Schwarz Method for
Nonlinear Complementarity Problems . . . 258--280
Changna Lu and
Jianxian Qiu Simulations of Shallow Water Equations
with Finite Difference Lax--Wendroff
Weighted Essentially Non-oscillatory
Schemes . . . . . . . . . . . . . . . . 281--302
Xiaobing Feng and
Michael Neilan Analysis of Galerkin Methods for the
Fully Nonlinear Monge--Amp\`ere Equation 303--327
Andreas Zeiser Fast Matrix-Vector Multiplication in the
Sparse-Grid Galerkin Method . . . . . . 328--346
Jehanzeb Hameed Chaudhry and
Stephen D. Bond and
Luke N. Olson Finite Element Approximation to a
Finite-Size Modified Poisson--Boltzmann
Equation . . . . . . . . . . . . . . . . 347--364
Andreas Dedner and
Robert Klöfkorn A Generic Stabilization Approach for
Higher Order Discontinuous Galerkin
Methods for Convection Dominated
Problems . . . . . . . . . . . . . . . . 365--388
K. Andrew Cliffe and
Edward J. C. Hall and
Paul Houston Adaptivity and a Posteriori Error
Control for Bifurcation Problems II:
Incompressible Fluid Flow in Open
Systems with $ Z_2 $ Symmetry . . . . . 389--418
Nehla Abdellatif and
Nejmeddine Chorfi and
Sihem Trabelsi Spectral Discretization of the
Axisymmetric Vorticity, Velocity and
Pressure Formulation of the Stokes
Problem . . . . . . . . . . . . . . . . 419--440
Rémi Abgrall and
Denise Aregba and
Christophe Berthon Preface . . . . . . . . . . . . . . . . 1--2
Patricio Bohorquez and
Martin Rentschler Hydrodynamic Instabilities in
Well-Balanced Finite Volume Schemes for
Frictional Shallow Water Equations. The
Kinematic Wave Case . . . . . . . . . . 3--15
M. J. Castro-Díaz and
E. D. Fernández-Nieto Numerical Treatment of the Loss of
Hyperbolicity of the Two-Layer
Shallow-Water System . . . . . . . . . . 16--40
Olivier Delestre and
Fabien Marche A Numerical Scheme for a Viscous Shallow
Water Model with Friction . . . . . . . 41--51
R. Donat and
A. Martinez-Gavara Hybrid Second Order Schemes for Scalar
Balance Laws . . . . . . . . . . . . . . 52--69
Michael Dumbser and
Eleuterio F. Toro A Simple Extension of the Osher Riemann
Solver to Non-conservative Hyperbolic
Systems . . . . . . . . . . . . . . . . 70--88
C. Bourdarias and
M. Ersoy and
S. Gerbi A Kinetic Scheme for Transient Mixed
Flows in Non Uniform Closed Pipes: a
Global Manner to Upwind All the Source
Terms . . . . . . . . . . . . . . . . . 89--104
F. Chazel and
D. Lannes and
F. Marche Numerical Simulation of Strongly
Nonlinear and Dispersive Waves Using a
Green--Naghdi Model . . . . . . . . . . 105--116
E. D. Fernández-Nieto and
M. J. Castro Díaz and
C. Parés On an Intermediate Field Capturing
Riemann Solver Based on a Parabolic
Viscosity Matrix for the Two-Layer
Shallow Water System . . . . . . . . . . 117--140
José M. Gallardo and
Sergio Ortega and
Marc de la Asunción Two-Dimensional Compact Third-Order
Polynomial Reconstructions. Solving
Nonconservative Hyperbolic Systems Using
GPUs . . . . . . . . . . . . . . . . . . 141--163
F. Coquel and
E. Godlewski Asymptotic Preserving Scheme for Euler
System with Large Friction . . . . . . . 164--172
Arturo Hidalgo and
Michael Dumbser ADER Schemes for Nonlinear Systems of
Stiff Advection--Diffusion-Reaction
Equations . . . . . . . . . . . . . . . 173--189
Gerardo Hernández-Dueñas and
Smadar Karni Shallow Water Flows in Channels . . . . 190--208
Randall J. LeVeque A Well-Balanced Path-Integral $f$-Wave
Method for Hyperbolic Problems with
Source Terms . . . . . . . . . . . . . . 209--226
A. Hundertmark-Zausková and
M. Lukácová-Medvid'ová Large Time Step Finite Volume Evolution
Galerkin Methods . . . . . . . . . . . . 227--240
A. Martinez-Gavara and
R. Donat A Hybrid Second Order Scheme for Shallow
Water Flows . . . . . . . . . . . . . . 241--257
T. Morales de Luna and
M. J. Castro Díaz and
C. Parés Madroñal A Duality Method for Sediment Transport
Based on a Modified Meyer--Peter & Müller
Model . . . . . . . . . . . . . . . . . 258--273
María Luz Muñoz-Ruiz and
Carlos Parés On the Convergence and Well-Balanced
Property of Path-Conservative Numerical
Schemes for Systems of Balance Laws . . 274--295
Vincent Perrier A Conservative Method for the Simulation
of the Isothermal Euler System with the
van-der-Waals Equation of State . . . . 296--303
M. Ricchiuto On the C-property and Generalized
C-property of Residual Distribution for
the Shallow Water Equations . . . . . . 304--318
L. Begnudelli and
G. Rosatti Hyperconcentrated $1$D Shallow Flows on
Fixed Bed with Geometrical Source Term
Due to a Bottom Step . . . . . . . . . . 319--332
Chiara Simeoni Remarks on the Consistency of Upwind
Source at Interface Schemes on
Nonuniform Grids . . . . . . . . . . . . 333--338
Yulong Xing and
Chi-Wang Shu and
Sebastian Noelle On the Advantage of Well-Balanced
Schemes for Moving-Water Equilibria of
the Shallow Water Equations . . . . . . 339--349
Maria Vittoria Salvetti and
Pierre Sagaut Preface . . . . . . . . . . . . . . . . 1--2
Luigi C. Berselli and
Paul F. Fischer and
Traian Iliescu Horizontal Large Eddy Simulation of
Stratified Mixing in a Lock--Exchange
System . . . . . . . . . . . . . . . . . 3--20
Jonathan Pietarila Graham and
Darryl D. Holm and
Pablo Mininni The Effect of Subfilter-Scale Physics on
Regularization Models . . . . . . . . . 21--34
Jean-Luc Guermond and
Richard Pasquetti and
Bojan Popov From Suitable Weak Solutions to Entropy
Viscosity . . . . . . . . . . . . . . . 35--50
A. M. Kempf and
B. J. Geurts and
T. Ma and
M. W. A. Pettit Quality Issues in Combustion LES . . . . 51--64
Johan Meyers Error-Landscape Assessment of Large-Eddy
Simulations: a Review of the Methodology 65--77
T. Poinsot and
M. Garcia and
J. M. Senoner and
L. Gicquel Numerical and Physical Instabilities in
Massively Parallel LES of Reacting Flows 78--93
Roel Verstappen When Does Eddy Viscosity Damp Subfilter
Scales Sufficiently? . . . . . . . . . . 94--110
Lucie Baudouin and
Julien Salomon and
Gabriel Turinici Analysis of the ``Toolkit'' Method for
the Time-Dependent Schrödinger Equation 111--136
Edwin M. Behrens and
J. Guzmán A New Family of Mixed Methods for the
Reissner--Mindlin Plate Model Based on a
System of First-Order Equations . . . . 137--166
Andrew Christlieb and
Benjamin Ong Implicit Parallel Time Integrators . . . 167--179
Jeremy Chamard and
Josef Otta and
David J. B. Lloyd Computation of Minimum Energy Paths for
Quasi-Linear Problems . . . . . . . . . 180--194
Lina Ye and
Guangwu Yan and
Tingting Li Numerical Method Based on the Lattice
Boltzmann Model for the
Kuramoto--Sivashinsky Equation . . . . . 195--210
Pedro Galán del Sastre and
Rodolfo Bermejo Error Analysis for $ h p $-FEM
Semi-Lagrangian Second Order BDF Method
for Convection-Dominated Diffusion
Problems . . . . . . . . . . . . . . . . 211--237
Ali Abbas and
Jean-Pierre Croisille A Fourth Order Hermitian Box-Scheme with
Fast Solver for the Poisson Problem in a
Square . . . . . . . . . . . . . . . . . 239--267
G. Simpson and
M. Spiegelman Solitary Wave Benchmarks in Magma
Dynamics . . . . . . . . . . . . . . . . 268--290
Roland Griesmaier and
Peter Monk Error Analysis for a Hybridizable
Discontinuous Galerkin Method for the
Helmholtz Equation . . . . . . . . . . . 291--310
Chunjia Bi and
Victor Ginting Two-Grid Discontinuous Galerkin Method
for Quasi-Linear Elliptic Problems . . . 311--331
Martin Frank and
Jens Lang and
Matthias Schäfer Adaptive Finite Element Simulation of
the Time-dependent Simplified $ P_N $
Equations . . . . . . . . . . . . . . . 332--350
Zhongyi Huang and
Xu Yang Tailored Finite Point Method for First
Order Wave Equation . . . . . . . . . . 351--366
Jiwei Zhang and
Houde Han and
Hermann Brunner Numerical Blow-up of Semilinear
Parabolic PDEs on Unbounded Domains in $
R^2 $ . . . . . . . . . . . . . . . . . 367--382
Luoping Chen and
Yanping Chen Two-Grid Method for Nonlinear
Reaction--Diffusion Equations by Mixed
Finite Element Methods . . . . . . . . . 383--401
Peter Constantin and
Ming-Chih Lai and
Ramjee Sharma New Numerical Results for the Surface
Quasi-Geostrophic Equation . . . . . . . 1--28
Xiangxiong Zhang and
Yinhua Xia and
Chi-Wang Shu Maximum-Principle-Satisfying and
Positivity-Preserving High Order
Discontinuous Galerkin Schemes for
Conservation Laws on Triangular Meshes 29--62
Truong Nguyen-Ba and
Huong Nguyen-Thu and
Thierry Giordano Strong-Stability-Preserving $7$-Stage
Hermite--Birkhoff Time-Discretization
Methods . . . . . . . . . . . . . . . . 63--90
Gerard Awanou Two Remarks on Rectangular Mixed Finite
Elements for Elasticity . . . . . . . . 91--102
Zhenning Cai and
Ruo Li and
Yanli Wang An Efficient NRxx Method for
Boltzmann--BGK Equation . . . . . . . . 103--119
Georges Kesserwani and
Qiuhua Liang Locally Limited and Fully Conserved
RKDG2 Shallow Water Solutions with
Wetting and Drying . . . . . . . . . . . 120--144
Chunlin Wu and
Juyong Zhang and
Yuping Duan and
Xue-Cheng Tai Augmented Lagrangian Method for Total
Variation Based Image Restoration and
Segmentation Over Triangulated Surfaces 145--166
Katharina Kormann and
Martin Kronbichler and
Bernhard Müller Derivation of Strictly Stable High Order
Difference Approximations for
Variable-Coefficient PDE . . . . . . . . 167--197
Simone Deparis and
A. Emil Lòvgren Stabilized Reduced Basis Approximation
of Incompressible Three-Dimensional
Navier--Stokes Equations in Parametrized
Deformed Domains . . . . . . . . . . . . 198--212
J. Laminie and
P. Poullet A Dynamic Penalty or Projection Method
for Incompressible Fluids . . . . . . . 213--234
Jooyoung Hahn and
Chunlin Wu and
Xue-Cheng Tai Augmented Lagrangian Method for
Generalized TV-Stokes Model . . . . . . 235--264
W. Hundsdorfer and
A. Mozartova and
M. N. Spijker Stepsize Restrictions for Boundedness
and Monotonicity of Multistep Methods 265--286
Luca Ded\`e Reduced Basis Method and Error
Estimation for Parametrized Optimal
Control Problems with Control
Constraints . . . . . . . . . . . . . . 287--305
Alen Alexanderian and
Oliver P. Le Ma\^\itre and
Habib N. Najm Multiscale Stochastic Preconditioners in
Non-intrusive Spectral Projection . . . 306--340
Jeremy E. Kozdon and
Eric M. Dunham and
Jan Nordström Interaction of Waves with Frictional
Interfaces Using Summation-by-Parts
Difference Operators: Weak Enforcement
of Nonlinear Boundary Conditions . . . . 341--367
Brian B. Christensen and
Michael B. Nielsen and
Ken Museth Out-of-Core Computations of
High-Resolution Level Sets by Means of
Code Transformation . . . . . . . . . . 368--404
Fatih Celiker and
Zhimin Zhang and
Huiqing Zhu Nodal Superconvergence of SDFEM for
Singularly Perturbed Problems . . . . . 405--433
A. Jameson and
P. E. Vincent and
P. Castonguay On the Non-linear Stability of Flux
Reconstruction Schemes . . . . . . . . . 434--445
Jianguo Xin and
Wei Cai Well-conditioned Orthonormal
Hierarchical $ \mathcal {L}_2 $ Bases on
$ R^n $ Simplicial Elements . . . . . . 446--461
S. P. van der Pijl and
C. W. Oosterlee An ENO-Based Method for Second-Order
Equations and Application to the Control
of Dike Levels . . . . . . . . . . . . . 462--492
Anne Gelb and
Rosemary Renaut and
Svetlana Roudenko Special Issue on Mathematical Methods in
Medical Imaging . . . . . . . . . . . . 493--494
Yang Wang and
Guo-Wei Wei and
Siyang Yang Mode Decomposition Evolution Equations 495--518
Xiaoqun Zhang and
Yujie Lu and
Tony Chan A Novel Sparsity Reconstruction Method
from Poisson Data for $3$D
Bioluminescence Tomography . . . . . . . 519--535
W. Stefan and
A. Viswanathan and
A. Gelb and
R. Renaut Sparsity Enforcing Edge Detection Method
for Blurred and Noisy Fourier data . . . 536--556
Lok Ming Lui and
Tsz Wai Wong and
Wei Zeng and
Xianfeng Gu Optimization of Surface Registrations
Using Beltrami Holomorphic Flow . . . . 557--585
Tungyou Lin and
Carole Le Guyader and
Ivo Dinov and
Paul Thompson Gene Expression Data to Mouse Atlas
Registration Using a Nonlinear
Elasticity Smoother and Landmark Points
Constraints . . . . . . . . . . . . . . 586--609
Christopher K. Turnes and
Justin Romberg Efficient Calculations of $3$-D FFTs on
Spiral Contours . . . . . . . . . . . . 610--628
Yang Wang and
Guo-Wei Wei and
Siyang Yang Iterative Filtering Decomposition Based
on Local Spectral Evolution Kernel . . . 629--664
Wolfgang Stefan and
Kewei Chen and
Hongbin Guo Wavelet-Based De-noising of Positron
Emission Tomography Scans . . . . . . . 665--677
Liangyue Ji and
Yan Xu Optimal Error Estimates of the Local
Discontinuous Galerkin Method for
Surface Diffusion of Graphs on Cartesian
Meshes . . . . . . . . . . . . . . . . . 1--27
J. L. Eftang and
D. B. P. Huynh and
D. J. Knezevic A Two-Step Certified Reduced Basis
Method . . . . . . . . . . . . . . . . . 28--58
P. Degond and
H. Liu and
D. Savelief and
M.-H. Vignal Numerical Approximation of the
Euler--Poisson--Boltzmann Model in the
Quasineutral Limit . . . . . . . . . . . 59--86
Ahmed Ratnani and
Eric Sonnendrücker An Arbitrary High-Order Spline Finite
Element Solver for the Time Domain
Maxwell Equations . . . . . . . . . . . 87--106
Qiang Zhang and
Fuzheng Gao A Fully-Discrete Local Discontinuous
Galerkin Method for Convection-Dominated
Sobolev Equation . . . . . . . . . . . . 107--134
B. Chabaud and
Q. Du A Hybrid Implicit-Explicit Adaptive
Multirate Numerical Scheme for
Time-Dependent Equations . . . . . . . . 135--157
Anne Gelb and
Taylor Hines Recovering Exponential Accuracy from
Non-harmonic Fourier Data Through
Spectral Reprojection . . . . . . . . . 158--182
Robert M. Kirby and
Spencer J. Sherwin and
Bernardo Cockburn To CG or to HDG: a Comparative Study . . 183--212
Fengyan Li On the Negative-Order Norm Accuracy of a
Local-Structure-Preserving LDG Method 213--223
P. Castonguay and
P. E. Vincent and
A. Jameson A New Class of High-Order Energy Stable
Flux Reconstruction Schemes for
Triangular Elements . . . . . . . . . . 224--256
Nehla Abdellatif and
Nejmeddine Chorfi and
Sihem Trabelsi Erratum to: Spectral Discretization of
the Axisymmetric Vorticity, Velocity and
Pressure Formulation of the Stokes
Problem . . . . . . . . . . . . . . . . 257--257
Lok Ming Lui and
Tsz Wai Wong and
Wei Zeng and
Xianfeng Gu Erratum to: Optimization of Surface
Registrations Using Beltrami Holomorphic
Flow . . . . . . . . . . . . . . . . . . 258--258
Xiaoqun Zhang and
Yujie Lu and
Tony Chan Erratum to: A Novel Sparsity
Reconstruction Method from Poisson Data
for $3$D Bioluminescence Tomography . . 259--259
Xiaoming Yuan Alternating Direction Method for
Covariance Selection Models . . . . . . 261--273
Tao Zhou and
Tao Tang Galerkin Methods for Stochastic
Hyperbolic Problems Using Bi-Orthogonal
Polynomials . . . . . . . . . . . . . . 274--292
Roland Pulch and
Dongbin Xiu Generalised Polynomial Chaos for a Class
of Linear Conservation Laws . . . . . . 293--312
Ken Alton and
Ian M. Mitchell An Ordered Upwind Method with
Precomputed Stencil and Monotone Node
Acceptance for Solving Static Convex
Hamilton--Jacobi Equations . . . . . . . 313--348
Christine Bernardi and
Tomás Chacón Rebollo and
Marco Restelli A Posteriori Analysis of a Positive
Streamwise Invariant Discretization of a
Convection-Diffusion Equation . . . . . 349--374
Aaron Katz and
Venkateswaran Sankaran An Efficient Correction Method to Obtain
a Formally Third-Order Accurate Flow
Solver for Node-Centered Unstructured
Grids . . . . . . . . . . . . . . . . . 375--393
J. Gopalakrishnan and
M. Oh Commuting Smoothed Projectors in
Weighted Norms with an Application to
Axisymmetric Maxwell Equations . . . . . 394--420
Bijaya Laxmi Panigrahi and
Gnaneshwar Nelakanti Richardson Extrapolation of Iterated
Discrete Galerkin Method for Eigenvalue
Problem of a Two Dimensional Compact
Integral Operator . . . . . . . . . . . 421--448
Hui Feng and
Fuxing Hu and
Rong Wang A New Mapped Weighted Essentially
Non-oscillatory Scheme . . . . . . . . . 449--473
Bernardo Llanas and
Sagrario Lantarón Edge Detection by Adaptive Splitting II.
The Three-Dimensional Case . . . . . . . 474--503
Dai-Qiang Chen and
Li-Zhi Cheng and
Fang Su A New TV-Stokes Model with Augmented
Lagrangian Method for Image Denoising
and Deconvolution . . . . . . . . . . . 505--526
Gang Li and
Changna Lu and
Jianxian Qiu Hybrid Well-balanced WENO Schemes with
Different Indicators for Shallow Water
Equations . . . . . . . . . . . . . . . 527--559
Kees van den Doel and
Uri Ascher The Chaotic Nature of Faster Gradient
Descent Methods . . . . . . . . . . . . 560--581
Bernardo Cockburn and
Wujun Zhang A Posteriori Error Estimates for HDG
Methods . . . . . . . . . . . . . . . . 582--607
A. Petersen and
A. Gelb and
R. Eubank Hypothesis Testing for Fourier Based
Edge Detection Methods . . . . . . . . . 608--630
Adityavikram Viswanathan and
Anne Gelb and
Douglas Cochran Iterative Design of Concentration
Factors for Jump Detection . . . . . . . 631--649
Ken Mattsson Summation by Parts Operators for Finite
Difference Approximations of
Second-Derivatives with Variable
Coefficients . . . . . . . . . . . . . . 650--682
Xinjuan Chen and
Jae-Hun Jung Matrix Stability of Multiquadric Radial
Basis Function Methods for Hyperbolic
Equations with Uniform Centers . . . . . 683--702
Björn Sjögreen High Order Finite Difference and Finite
Volume Methods for Advection on the
Sphere . . . . . . . . . . . . . . . . . 703--732
Yuanchang Sun and
Jack Xin A Recursive Sparse Blind Source
Separation Method and Its Application to
Correlated Data in NMR Spectroscopy of
Biofluids . . . . . . . . . . . . . . . 733--753
Ken Mattsson Erratum to: Summation by Parts Operators
for Finite Difference Approximations of
Second-Derivatives with Variable
Coefficients . . . . . . . . . . . . . . 754--754
Jianying Zhang and
Guangwu Yan A Lattice Boltzmann Model for the
Reaction--Diffusion Equations with
Higher-Order Accuracy . . . . . . . . . 1--16
Björn Sjögreen and
N. Anders Petersson A Fourth Order Accurate Finite
Difference Scheme for the Elastic Wave
Equation in Second Order Formulation . . 17--48
Fatih Celiker and
Li Fan and
Sheng Zhang and
Zhimin Zhang Locking-Free Optimal Discontinuous
Galerkin Methods for a Naghdi-Type Arch
Model . . . . . . . . . . . . . . . . . 49--84
Hanieh Mirzaee and
Jennifer K. Ryan and
Robert M. Kirby Efficient Implementation of
Smoothness-Increasing
Accuracy--Conserving (SIAC) Filters for
Discontinuous Galerkin Solutions . . . . 85--112
Slimane Adjerid and
Mahboub Baccouch A Superconvergent Local Discontinuous
Galerkin Method for Elliptic Problems 113--152
K. Andrew Cliffe and
Edward J. C. Hall and
Paul Houston Adaptivity and a Posteriori Error
Control for Bifurcation Problems III:
Incompressible Fluid Flow in Open
Systems with $ O(2) $ Symmetry . . . . . 153--179
Rodney Josué Biezuner and
Jed Brown and
Grey Ercole Computing the First Eigenpair of the
$p$-Laplacian via Inverse Iteration of
Sublinear Supersolutions . . . . . . . . 180--201
Burak Aksoylu and
Stephen D. Bond and
Eric C. Cyr Goal-Oriented Adaptivity and Multilevel
Preconditioning for the
Poisson--Boltzmann Equation . . . . . . 202--225
Zhong-qing Wang and
Ben-yu Guo Legendre--Gauss--Radau Collocation
Method for Solving Initial Value
Problems of First Order Ordinary
Differential Equations . . . . . . . . . 226--255
Bernardo Cockburn and
Jintao Cui Divergence-Free HDG Methods for the
Vorticity--Velocity Formulation of the
Stokes Problem . . . . . . . . . . . . . 256--270
Martin K. Bernauer and
Roland Herzog Implementation of an X--FEM Solver for
the Classical Two-Phase Stefan Problem 271--293
Ludovic Gouden\`ege and
Daniel Martin and
Grégory Vial High Order Finite Element Calculations
for the Cahn--Hilliard Equation . . . . 294--321
Rommel Bustinza and
Francisco-Javier Sayas Error Estimates for an LDG Method
Applied to Signorini Type Problems . . . 322--339
Marta D'Elia and
Mauro Perego and
Alessandro Veneziani A Variational Data Assimilation
Procedure for the Incompressible
Navier--Stokes Equations in Hemodynamics 340--359
Songting Luo and
Jianliang Qian Fast Sweeping Methods for Factored
Anisotropic Eikonal Equations:
Multiplicative and Additive Factors . . 360--382
D. Boffi and
N. Cavallini and
F. Gardini and
L. Gastaldi Local Mass Conservation of Stokes Finite
Elements . . . . . . . . . . . . . . . . 383--400
Harish Kumar and
Siddhartha Mishra Entropy Stable Numerical Schemes for
Two-Fluid Plasma Equations . . . . . . . 401--425
Jun Hu and
Yunqing Huang and
Quan Shen A High Accuracy Post-processing
Algorithm for the Eigenvalues of
Elliptic Operators . . . . . . . . . . . 426--445
Marco Schauer and
Jose E. Roman and
Enrique S. Quintana-Ortí Parallel Computation of $3$-D
Soil-Structure Interaction in Time
Domain with a Coupled FEM/SBFEM Approach 446--467
J. C. Dietrich and
S. Tanaka and
J. J. Westerink and
C. N. Dawson Performance of the Unstructured-Mesh,
SWAN+ADCIRC Model in Computing Hurricane
Waves and Surge . . . . . . . . . . . . 468--497
Feng Chen and
Jie Shen and
Haijun Yu A New Spectral Element Method for
Pricing European Options Under the
Black--Scholes and Merton Jump Diffusion
Models . . . . . . . . . . . . . . . . . 499--518
Xinlong Feng and
Rongfei Li and
Yinnian He and
Demin Liu $ P_1 $-Nonconforming Quadrilateral
Finite Volume Methods for the Semilinear
Elliptic Equations . . . . . . . . . . . 519--545
Wenbin Chen and
Sidafa Conde and
Cheng Wang and
Xiaoming Wang A Linear Energy Stable Scheme for a Thin
Film Model Without Slope Selection . . . 546--562
Hao Pan and
Hongxing Rui Mixed Element Method for Two-Dimensional
Darcy--Forchheimer Model . . . . . . . . 563--587
Tinggang Zhao and
Yujiang Wu and
Heping Ma Error Analysis of Chebyshev--Legendre
Pseudo-spectral Method for a Class of
Nonclassical Parabolic Equation . . . . 588--602
Tormod Bjòntegaard and
Einar M. Rònquist and
Òystein Tråsdahl Spectral Approximation of Partial
Differential Equations in Highly
Distorted Domains . . . . . . . . . . . 603--618
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Static Two-Grid Mixed Finite-Element
Approximations to the Navier--Stokes
Equations . . . . . . . . . . . . . . . 619--637
Mengping Zhang and
Jue Yan Fourier Type Error Analysis of the
Direct Discontinuous Galerkin Method and
Its Variations for Diffusion Equations 638--655
Jianying Zhang and
Guangwu Yan Numerical Studies Based on Higher-Order
Accuracy Lattice Boltzmann Model for the
Complex Ginzburg--Landau Equation . . . 656--674
Lorenzo Botti Influence of Reference-to-Physical Frame
Mappings on Approximation Properties of
Discontinuous Piecewise Polynomial
Spaces . . . . . . . . . . . . . . . . . 675--703
Sigal Gottlieb and
Adi Ditkowski Preface . . . . . . . . . . . . . . . . 1--2
Qingshan Chen and
Youngjoon Hong and
Roger Temam Analysis of a Penalty Method . . . . . . 3--34
Neta Corem and
Adi Ditkowski New Analysis of the Du Fort--Frankel
Methods . . . . . . . . . . . . . . . . 35--54
D. Fishelov and
M. Ben-Artzi and
J.-P. Croisille Recent Advances in the Study of a
Fourth-Order Compact Scheme for the
One-Dimensional Biharmonic Equation . . 55--79
Zhen Gao and
Wai Sun Don and
Zhiqiu Li High Order Weighted Essentially
Non-oscillation Schemes for
Two-Dimensional Detonation Wave
Simulations . . . . . . . . . . . . . . 80--101
Sigal Gottlieb and
Cheng Wang Stability and Convergence Analysis of
Fully Discrete Fourier Collocation
Spectral Method for $3$-D Viscous
Burgers' Equation . . . . . . . . . . . 102--128
James King and
Hanieh Mirzaee and
Jennifer K. Ryan Smoothness-Increasing
Accuracy-Conserving (SIAC) Filtering for
Discontinuous Galerkin Solutions:
Improved Errors Versus Higher-Order
Accuracy . . . . . . . . . . . . . . . . 129--149
M. Medvinsky and
S. Tsynkov and
E. Turkel The Method of Difference Potentials for
the Helmholtz Equation Using Compact
High Order Schemes . . . . . . . . . . . 150--193
Z. Schuss The Narrow Escape Problem --- a Short
Review of Recent Results . . . . . . . . 194--210
Hillel Tal-Ezer and
Ronnie Kosloff and
Ido Schaefer New, Highly Accurate Propagator for the
Linear and Nonlinear Schrödinger Equation 211--221
Tao Xiong and
Chi-Wang Shu and
Mengping Zhang WENO Scheme with Subcell Resolution for
Computing Nonconservative Euler
Equations with Applications to
One-Dimensional Compressible Two-Medium
Flows . . . . . . . . . . . . . . . . . 222--247
Huimin Lin and
Zhenli Xu and
Huazhong Tang and
Wei Cai Image Approximations to Electrostatic
Potentials in Layered
Electrolytes/Dielectrics and an
Ion-Channel Model . . . . . . . . . . . 249--267
Sehun Chun Method of Moving Frames to Solve
Conservation Laws on Curved Surfaces . . 268--294
N. Kishore Kumar and
G. Naga Raju Nonconforming Least-Squares Method for
Elliptic Partial Differential Equations
with Smooth Interfaces . . . . . . . . . 295--319
Faker Ben Belgacem and
Duc Thang Du and
Faten Jelassi Local Convergence of the Lavrentiev
Method for the Cauchy Problem via a
Carleman Inequality . . . . . . . . . . 320--341
Sebastian Kestler and
Karsten Urban Adaptive Wavelet Methods on Unbounded
Domains . . . . . . . . . . . . . . . . 342--376
Peiqi Huang and
Jinru Chen and
Mingchao Cai A Mixed and Nonconforming FEM with
Nonmatching Meshes for a Coupled
Stokes--Darcy Model . . . . . . . . . . 377--394
Wenrui Hao and
Jonathan D. Hauenstein and
Bei Hu and
Yuan Liu Continuation Along Bifurcation Branches
for a Tumor Model with a Necrotic Core 395--413
Ziqing Xie and
Xianjuan Li and
Tao Tang Convergence Analysis of Spectral
Galerkin Methods for Volterra Type
Integral Equations . . . . . . . . . . . 414--434
Chenliang Li and
Zhonghua Qiao A Fast Preconditioned Iterative
Algorithm for the Electromagnetic
Scattering from a Large Cavity . . . . . 435--450
Chao Zhang and
Ben-yu Guo Domain Decomposition Spectral Method for
Mixed Inhomogeneous Boundary Value
Problems of High Order Differential
Equations on Unbounded Domains . . . . . 451--480
Sehun Chun Erratum to: Method of Moving Frames to
Solve Conservation Laws on Curved
Surfaces . . . . . . . . . . . . . . . . 481--481
M. Medvinsky and
S. Tsynkov and
E. Turkel Erratum to: The Method of Difference
Potentials for the Helmholtz Equation
Using Compact High Order Schemes . . . . 482--482
Dmitriy Leykekhman Investigation of Commutative Properties
of Discontinuous Galerkin Methods in PDE
Constrained Optimal Control Problems . . 483--511
Huang Hongying and
Yang Ju'e and
Yu Dehao A Coupling of Local Discontinuous
Galerkin and Natural Boundary Element
Method for Exterior Problems . . . . . . 512--527
A. Nissen and
G. Kreiss and
M. Gerritsen Stability at Nonconforming Grid
Interfaces for a High Order
Discretization of the Schrödinger
Equation . . . . . . . . . . . . . . . . 528--551
J. H. M. ten Thije Boonkkamp and
J. van Dijk and
L. Liu Extension of the Complete Flux Scheme to
Systems of Conservation Laws . . . . . . 552--568
Huilin Lai and
Changfeng Ma Numerical Study of the Nonlinear
Combined Sine-Cosine--Gordon Equation
with the Lattice Boltzmann Method . . . 569--585
Veerle Ledoux and
Marnix Van Daele Interpolatory Quadrature Rules for
Oscillatory Integrals . . . . . . . . . 586--607
C. Acary-Robert and
E. D. Fernández-Nieto and
G. Narbona-Reina A Well-balanced Finite Volume-Augmented
Lagrangian Method for an Integrated
Herschel--Bulkley Model . . . . . . . . 608--641
Kenneth Duru and
Gunilla Kreiss On the Accuracy and Stability of the
Perfectly Matched Layer in Transient
Waveguides . . . . . . . . . . . . . . . 642--671
Yunxia Wei and
Yanping Chen Legendre Spectral Collocation Methods
for Pantograph Volterra
Delay--Integro-Differential Equations 672--688
Yekaterina Epshteyn Upwind-Difference Potentials Method for
Patlak--Keller--Segel Chemotaxis Model 689--713
Amir Nejat and
Vahid Abdollahi A Critical Study of the Compressible
Lattice Boltzmann Methods for Riemann
Problem . . . . . . . . . . . . . . . . 1--20
Gregor J. Gassner An Analysis of the Dissipation and
Dispersion Errors of the $ P_N P_M $
Schemes . . . . . . . . . . . . . . . . 21--44
Sangita Yadav and
Amiya K. Pani and
Neela Nataraj Superconvergent Discontinuous Galerkin
Methods for Linear Non-selfadjoint and
Indefinite Elliptic Problems . . . . . . 45--76
Qingsong Zou A Novel Hierarchial Error Estimate for
Elliptic Obstacle Problems . . . . . . . 77--96
Shuying Zhai and
Xinlong Feng and
Yinnian He A Family of Fourth-Order and Sixth-Order
Compact Difference Schemes for the
Three-Dimensional Poisson Equation . . . 97--120
Jichun Li and
Yunqing Huang and
Wei Yang Numerical Study of the Plasma--Lorentz
Model in Metamaterials . . . . . . . . . 121--144
Avram Sidi Compact Numerical Quadrature Formulas
for Hypersingular Integrals and Integral
Equations . . . . . . . . . . . . . . . 145--176
Thirupathi Gudi and
Hari Shanker Gupta and
Neela Nataraj Analysis of an Interior Penalty Method
for Fourth Order Problems on Polygonal
Domains . . . . . . . . . . . . . . . . 177--199
Michael Neilan Quadratic Finite Element Approximations
of the Monge--Amp\`ere Equation . . . . 200--226
Meilin Yu and
Z. J. Wang On the Connection Between the Correction
and Weighting Functions in the
Correction Procedure via Reconstruction
Method . . . . . . . . . . . . . . . . . 227--244
Chi-Wang Shu Preface . . . . . . . . . . . . . . . . 245--246
G. Ariel and
B. Engquist and
S. Kim and
Y. Lee and
R. Tsai A Multiscale Method for Highly
Oscillatory Dynamical Systems Using a
Poincaré Map Type Technique . . . . . . . 247--268
Martin Benning and
Christoph Brune and
Martin Burger \ldots Higher-Order TV Methods --- Enhancement
via Bregman Iteration . . . . . . . . . 269--310
Barna L. Bihari Transactional Memory for Unstructured
Mesh Simulations . . . . . . . . . . . . 311--332
Bin Dong and
Jia Li and
Zuowei Shen X-Ray CT Image Reconstruction via
Wavelet Frame Based Regularization and
Radon Domain Inpainting . . . . . . . . 333--349
Bin Dong and
Yong Zhang An Efficient Algorithm for $ l_0 $
Minimization in Wavelet Frame Based
Image Restoration . . . . . . . . . . . 350--368
Frédéric Gibou and
Chohong Min and
Ron Fedkiw High Resolution Sharp Computational
Methods for Elliptic and Parabolic
Problems in Complex Geometries . . . . . 369--413
Youngsoo Ha and
Chang Ho Kim and
Myungjoo Kang Simulations of Supersonic Astrophysical
Jets and Their Environments Using Level
Set Methods . . . . . . . . . . . . . . 414--427
Bo Huang and
Shiqian Ma and
Donald Goldfarb Accelerated Linearized Bregman Method 428--453
Matthew Jemison and
Eva Loch and
Mark Sussman \ldots A Coupled Level Set-Moment of Fluid
Method for Incompressible Two-Phase
Flows . . . . . . . . . . . . . . . . . 454--491
Chiu-Yen Kao and
Shu Su Efficient Rearrangement Algorithms for
Shape Optimization on Elliptic
Eigenvalue Problems . . . . . . . . . . 492--512
Tijana Kosti\'c and
Andrea Bertozzi Statistical Density Estimation Using
Threshold Dynamics for Geometric Motion 513--530
Liangyue Ji and
Yan Xu and
Jennifer K. Ryan Negative-Order Norm Estimates for
Nonlinear Hyperbolic Conservation Laws 531--548
Andreas Langer and
Stanley Osher and
Carola-Bibiane Schönlieb Bregmanized Domain Decomposition for
Image Restoration . . . . . . . . . . . 549--576
Jian Liang and
Frederick Park and
Hongkai Zhao Robust and Efficient Implicit Surface
Reconstruction for Point Clouds Based on
Convexified Image Segmentation . . . . . 577--602
Yuan Liu and
Yong-Tao Zhang A Robust Reconstruction for Unstructured
WENO Schemes . . . . . . . . . . . . . . 603--621
Ryo Takei and
Richard Tsai Optimal Trajectories of Curvature
Constrained Motion in the
Hamilton--Jacobi Formulation . . . . . . 622--644
Yulong Xing and
Chi-Wang Shu High Order Well-Balanced WENO Scheme for
the Gas Dynamics Equations Under
Gravitational Fields . . . . . . . . . . 645--662
Jue Yan A New Nonsymmetric Discontinuous
Galerkin Method for Time Dependent
Convection Diffusion Equations . . . . . 663--683
Wotao Yin and
Stanley Osher Error Forgetting of Bregman Iteration 684--695
Maxime Theillard and
Chris H. Rycroft and
Frédéric Gibou A Multigrid Method on Non-Graded
Adaptive Octree and Quadtree Cartesian
Grids . . . . . . . . . . . . . . . . . 1--15
Kuan Xu and
Shidong Jiang A Bootstrap Method for Sum-of-Poles
Approximations . . . . . . . . . . . . . 16--39
K. R. Arun and
M. Lukácová-Medvidová A Characteristics Based Genuinely
Multidimensional Discrete Kinetic Scheme
for the Euler Equations . . . . . . . . 40--64
Zohra Hammouch and
Gérard Labrosse and
Serge Gauthier Anelastic Stokes Eigenmodes in Infinite
Channel . . . . . . . . . . . . . . . . 65--91
Jeremy E. Kozdon and
Eric M. Dunham and
Jan Nordström Simulation of Dynamic Earthquake
Ruptures in Complex Geometries Using
High-Order Finite Difference Methods . . 92--124
Jun Hu and
Jinchao Xu Convergence and Optimality of the
Adaptive Nonconforming Linear Element
Method for the Stokes Problem . . . . . 125--148
Michael Griebel and
Daniel Wissel Fast Approximation of the Discrete Gauss
Transform in Higher Dimensions . . . . . 149--172
A. Nissen and
G. Kreiss and
M. Gerritsen High Order Stable Finite Difference
Methods for the Schrödinger Equation . . 173--199
Christopher Davis and
June G. Kim and
Hae-Soo Oh \ldots Meshfree Particle Methods in the
Framework of Boundary Element Methods
for the Helmholtz Equation . . . . . . . 200--230
Christophe Besse and
Fabrice Deluzet and
Claudia Negulescu \ldots Efficient Numerical Methods for Strongly
Anisotropic Elliptic Equations . . . . . 231--254
Lina Song and
Yanren Hou and
Haibiao Zheng Adaptive Local Postprocessing Finite
Element Method for the Navier--Stokes
Equations . . . . . . . . . . . . . . . 255--267
Christophe Berthon and
Céline Sarazin and
Rodolphe Turpault Space-time Generalized Riemann Problem
Solvers of Order $k$ for Linear
Advection with Unrestricted Time Step 268--308
Ali W. K. Sangawi and
Ali H. M. Murid and
M. M. S. Nasser Radial Slit Maps of Bounded Multiply
Connected Regions . . . . . . . . . . . 309--326
Tao Sun and
Ben-yu Guo Generalized Jacobi Approximation in
Multiple Dimensions and Its Applications 327--350
Zhen Gao and
Wai Sun Don Mapped Hybrid Central-WENO Finite
Difference Scheme for Detonation Waves
Simulations . . . . . . . . . . . . . . 351--371
Gang Bao and
Guanghui Hu and
Di Liu Numerical Solution of the Kohn--Sham
Equation by Finite Element Methods with
an Adaptive Mesh Redistribution
Technique . . . . . . . . . . . . . . . 372--391
Aycil Cesmelioglu and
Bernardo Cockburn and
Ngoc Cuong Nguyen \ldots Analysis of HDG Methods for Oseen
Equations . . . . . . . . . . . . . . . 392--431
Jun Fang and
Xingyu Gao and
Aihui Zhou A Finite Element Recovery Approach to
Eigenvalue Approximations with
Applications to Electronic Structure
Calculations . . . . . . . . . . . . . . 432--454
Lihua Shen and
Jack Xin and
Aihui Zhou Finite Element Computation of KPP Front
Speeds in Cellular and Cat's Eye Flows 455--470
Scott Congreve and
Paul Houston and
Thomas P. Wihler Two-Grid $ h p $-Version Discontinuous
Galerkin Finite Element Methods for
Second-Order Quasilinear Elliptic PDEs 471--497
Jorge Balbás and
Smadar Karni A Non-oscillatory Central Scheme for
One-Dimensional Two-Layer Shallow Water
Flows along Channels with Varying Width 499--528
Tsung-Ming Huang and
Yueh-Cheng Kuo and
Weichung Wang Computing Extremal Eigenvalues for
Three-Dimensional Photonic Crystals with
Wave Vectors Near the Brillouin Zone
Center . . . . . . . . . . . . . . . . . 529--551
He Yang and
Fengyan Li and
Jianxian Qiu Dispersion and Dissipation Errors of Two
Fully Discrete Discontinuous Galerkin
Methods . . . . . . . . . . . . . . . . 552--574
Olivier Bokanowski and
Jochen Garcke and
Michael Griebel \ldots An Adaptive Sparse Grid Semi-Lagrangian
Scheme for First Order Hamilton--Jacobi
Bellman Equations . . . . . . . . . . . 575--605
Jun Zhu and
Jianxian Qiu WENO Schemes and Their Application as
Limiters for RKDG Methods Based on
Trigonometric Approximation Spaces . . . 606--644
Hong-Ru Chen and
Shao-Chun Chen and
Zhong-Hua Qiao $ C^0 $-Nonconforming Triangular Prism
Elements for the Three-Dimensional
Fourth Order Elliptic Problem . . . . . 645--658
Chunjia Bi and
Victor Ginting A Posteriori Error Estimates of
Discontinuous Galerkin Method for
Nonmonotone Quasi-linear Elliptic
Problems . . . . . . . . . . . . . . . . 659--687
Eduardo Abreu and
Duilio Conceição Numerical Modeling of Degenerate
Equations in Porous Media Flow . . . . . 688--717
Yanlai Chen and
Sigal Gottlieb Reduced Collocation Methods: Reduced
Basis Methods in the Collocation
Framework . . . . . . . . . . . . . . . 718--737
S. C. Brenner and
J. Gedicke and
L.-Y. Sung An Adaptive $ P_1 $ Finite Element
Method for Two-Dimensional Maxwell's
Equations . . . . . . . . . . . . . . . 738--754
Tao Tang and
Hehu Xie and
Xiaobo Yin High-Order Convergence of Spectral
Deferred Correction Methods on General
Quadrature Nodes . . . . . . . . . . . . 1--13
Paola F. Antonietti and
Nadia Bigoni and
Marco Verani Mimetic Discretizations of Elliptic
Control Problems . . . . . . . . . . . . 14--27
Emil M. Constantinescu and
Adrian Sandu Extrapolated Multirate Methods for
Differential Equations with Multiple
Time Scales . . . . . . . . . . . . . . 28--44
Han Zhou and
WenYi Tian and
Weihua Deng Quasi-Compact Finite Difference Schemes
for Space Fractional Diffusion Equations 45--66
Jian Fang and
Zhaorui Li and
Lipeng Lu An Optimized Low-Dissipation
Monotonicity-Preserving Scheme for
Numerical Simulations of High-Speed
Turbulent Flows . . . . . . . . . . . . 67--95
A. Karageorghis and
L. Marin Efficient MFS Algorithms for Problems in
Thermoelasticity . . . . . . . . . . . . 96--121
Rui Du and
Wenwen Liu A New Multiple-relaxation-time Lattice
Boltzmann Method for Natural Convection 122--130
Deepjyoti Goswami and
Amiya K. Pani and
Sangita Yadav Optimal Error Estimates of Two Mixed
Finite Element Methods for Parabolic
Integro-Differential Equations with
Nonsmooth Initial Data . . . . . . . . . 131--164
P. X. Yu and
Zhen F. Tian A compact scheme for the
streamfunction-velocity formulation of
the $2$D steady incompressible
Navier--Stokes equations in polar
coordinates . . . . . . . . . . . . . . 165--189
Stéphane Descombes and
Stéphane Lanteri and
Ludovic Moya Locally Implicit Time Integration
Strategies in a Discontinuous Galerkin
Method for Maxwell's Equations . . . . . 190--218
Johnny Guzmán and
Abner J. Salgado and
Francisco-Javier Sayas A Note on the
Ladyzenskaja--Babuska--Brezzi Condition 219--229
L. A. Hegele, Jr. and
K. Mattila and
P. C. Philippi Rectangular Lattice-Boltzmann Schemes
with BGK-Collision Operator . . . . . . 230--242
Jun Liu and
Shingyu Leung A Splitting Algorithm for Image
Segmentation on Manifolds Represented by
the Grid Based Particle Method . . . . . 243--266
Andreas Bollermann and
Guoxian Chen and
Alexander Kurganov and
Sebastian Noelle A Well-Balanced Reconstruction of
Wet/Dry Fronts for the Shallow Water
Equations . . . . . . . . . . . . . . . 267--290
Xuehai Huang and
Jianguo Huang The Compact Discontinuous Galerkin
Method for Nearly Incompressible Linear
Elasticity . . . . . . . . . . . . . . . 291--318
Yingda Cheng and
Irene M. Gamba and
Philip J. Morrison Study of conservation and recurrence of
Runge--Kutta discontinuous Galerkin
schemes for Vlasov--Poisson systems . . 319--349
Wenrui Hao and
Bei Hu and
Andrew J. Sommese Cell Cycle Control and Bifurcation for a
Free Boundary Problem Modeling Tissue
Growth . . . . . . . . . . . . . . . . . 350--365
Gaurav Khanna High-Precision Numerical Simulations on
a CUDA GPU: Kerr Black Hole Tails . . . 366--380
Jincheng Ren and
Zhi-zhong Sun Numerical Algorithm With High Spatial
Accuracy for the Fractional
Diffusion-Wave Equation With Neumann
Boundary Conditions . . . . . . . . . . 381--408
Ming Wang and
Long Chen Multigrid Methods for the Stokes
Equations using Distributive
Gauss--Seidel Relaxations based on the
Least Squares Commutator . . . . . . . . 409--431
Ming Yan and
Yi Yang and
Stanley Osher Exact Low-Rank Matrix Completion from
Sparsely Corrupted Entries Via Adaptive
Outlier Pursuit . . . . . . . . . . . . 433--449
Ruisheng Qi and
Xiaoyuan Yang Weak Convergence of Finite Element
Method for Stochastic Elastic Equation
Driven By Additive Noise . . . . . . . . 450--470
David R. Martin and
Lothar Reichel Projected Tikhonov Regularization of
Large-Scale Discrete Ill-Posed Problems 471--493
Xiangling Chen and
Rui Wang and
Yuesheng Xu Fast Fourier--Galerkin Methods for
Nonlinear Boundary Integral Equations 494--514
Myeongmin Kang and
Sangwoon Yun and
Hyenkyun Woo and
Myungjoo Kang Accelerated Bregman Method for Linearly
Constrained $ \ell_1 $--$ \ell_2 $
Minimization . . . . . . . . . . . . . . 515--534
Edward J. Fuselier and
Grady B. Wright A High-Order Kernel Method for Diffusion
and Reaction--Diffusion Equations on
Surfaces . . . . . . . . . . . . . . . . 535--565
Waixiang Cao and
Zhimin Zhang and
Qingsong Zou Superconvergence of Any Order Finite
Volume Schemes for $1$D General Elliptic
Equations . . . . . . . . . . . . . . . 566--590
An Le and
Zhi-Qiang Wang and
Jianxin Zhou Finding Multiple Solutions to Elliptic
PDE with Nonlinear Boundary Conditions 591--615
Ruo Li and
Shuonan Wu $H$-adaptive Mesh Method with Double
Tolerance Adaptive Strategy for
Hyperbolic Conservation Laws . . . . . . 616--636
Dong-yang Shi and
Chao Xu and
Jin-huan Chen Anisotropic Nonconforming $ {\rm
EQ}_1^{\rm rot} $ Quadrilateral Finite
Element Approximation to Second Order
Elliptic Problems . . . . . . . . . . . 637--653
J. W. Banks and
T. D. Aslam Richardson Extrapolation for Linearly
Degenerate Discontinuities . . . . . . . 1--18
Yulong Xing and
Xiangxiong Zhang Positivity-Preserving Well-Balanced
Discontinuous Galerkin Methods for the
Shallow Water Equations on Unstructured
Triangular Meshes . . . . . . . . . . . 19--41
A. N. Kudryavtsev and
A. A. Shershnev A Numerical Method for Simulation of
Microflows by Solving Directly Kinetic
Equations with WENO Schemes . . . . . . 42--73
Gang Wu and
Ying Zhang and
Yimin Wei Accelerating the Arnoldi-Type Algorithm
for the PageRank Problem and the
ProteinRank Problem . . . . . . . . . . 74--104
Constantin Bacuta and
Lu Shu Multilevel Gradient Uzawa Algorithms for
Symmetric Saddle Point Problems . . . . 105--123
Yinnian He and
Yan Zhang and
Hui Xu Two-Level Newton's Method for Nonlinear
Elliptic PDEs . . . . . . . . . . . . . 124--145
G. Rubio and
F. Fraysse and
J. de Vicente and
E. Valero The Estimation of Truncation Error by $
\tau $-Estimation for Chebyshev Spectral
Collocation Method . . . . . . . . . . . 146--173
Antonio Márquez and
Salim Meddahi and
Francisco-Javier Sayas A Decoupled Preconditioning Technique
for a Mixed Stokes--Darcy Model . . . . 174--192
Jean-Pierre Croisille Hermitian Compact Interpolation on the
Cubed-Sphere Grid . . . . . . . . . . . 193--212
Roberto Ferretti Stability of Some Generalized Godunov
Schemes With Linear High-Order
Reconstructions . . . . . . . . . . . . 213--228
Xin-min Xiang and
Zhong-qing Wang Generalized Hermite Approximations and
Spectral Method for Partial Differential
Equations in Multiple Dimensions . . . . 229--253
Johan Malm and
Philipp Schlatter and
Paul F. Fischer and
Dan S. Henningson Stabilization of the Spectral Element
Method in Convection Dominated Flows by
Recovery of Skew-Symmetry . . . . . . . 254--277
Xihua Xu and
Guoxi Ni and
Song Jiang A High-Order Moving Mesh Kinetic Scheme
Based on WENO Reconstruction for
Compressible Flows on Unstructured
Meshes . . . . . . . . . . . . . . . . . 278--299
Francesco Calabr\`o Numerical Treatment of Elliptic Problems
Nonlinearly Coupled Through the
Interface . . . . . . . . . . . . . . . 300--312
Andrea Cangiani and
John Chapman and
Emmanuil Georgoulis and
Max Jensen On the Stability of
Continuous--Discontinuous Galerkin
Methods for
Advection--Diffusion-Reaction Problems 313--330
Xinming Wu and
Wenbin Chen Error Estimates of the Finite Element
Method for Interior Transmission
Problems . . . . . . . . . . . . . . . . 331--348
Fang Li and
Tieyong Zeng Image Restoration via Tight Frame
Regularization and Local Constraints . . 349--371
John P. Boyd and
Gregor Gassner and
Burhan A. Sadiq The Nonconvergence of $h$-Refinement in
Prolate Elements . . . . . . . . . . . . 372--389
Pierre Garreau and
David Kopriva A Spectral Element Framework for Option
Pricing Under General Exponential Lévy
Processes . . . . . . . . . . . . . . . 390--413
Wei Zhu and
Xue-Cheng Tai and
Tony Chan Image Segmentation Using Euler's
Elastica as the Regularization . . . . . 414--438
Sebastian Kestler and
Rob Stevenson An Efficient Approximate Residual
Evaluation in the Adaptive Tensor
Product Wavelet Method . . . . . . . . . 439--463
Michiel E. Hochstenbach Probabilistic Upper Bounds for the
Matrix Two-Norm . . . . . . . . . . . . 464--476
Sivaram Ambikasaran and
Eric Darve An $ \mathcal O (N \log N) $ Fast Direct
Solver for Partial Hierarchically
Semi-Separable Matrices . . . . . . . . 477--501
Zhongying Chen and
Guangqing Long and
Gnaneshwar Nelakanti and
Yongdong Zhang Iterated Fast Collocation Methods for
Integral Equations of the Second Kind 502--517
Inmaculada Higueras Strong Stability for Runge--Kutta
Schemes on a Class of Nonlinear Problems 518--535
J. M. Melenk and
A. Parsania and
S. Sauter General DG-Methods for Highly Indefinite
Helmholtz Problems . . . . . . . . . . . 536--581
Misun Min and
Paul Fischer An Efficient High-Order Time Integration
Method for Spectral-Element
Discontinuous Galerkin Simulations in
Electromagnetics . . . . . . . . . . . . 582--603
Harbir Antil and
Scott E. Field and
Frank Herrmann and
Ricardo H. Nochetto and
Manuel Tiglio Two-Step Greedy Algorithm for Reduced
Order Quadratures . . . . . . . . . . . 604--637
Jun Fang and
Xingyu Gao and
Aihui Zhou A Symmetry-Based Decomposition Approach
to Eigenvalue Problems . . . . . . . . . 638--669
Jing An and
Jie Shen A Spectral-Element Method for
Transmission Eigenvalue Problems . . . . 670--688
Zhiyong Si and
Xiaogang Song and
Pengzhan Huang Modified Characteristics Gauge--Uzawa
Finite Element Method for Time Dependent
Conduction--Convection Problems . . . . 1--24
B. Fabr\`eges and
B. Maury Approximation of Single Layer
Distributions by Dirac Masses in Finite
Element Computations . . . . . . . . . . 25--40
Chao Liang and
Zhengfu Xu Parametrized Maximum Principle
Preserving Flux Limiters for High Order
Schemes Solving Multi-Dimensional Scalar
Hyperbolic Conservation Laws . . . . . . 41--60
Magnus Svärd and
Hatice Özcan Entropy-Stable Schemes for the Euler
Equations with Far-Field and Wall
Boundary Conditions . . . . . . . . . . 61--89
Xiaozhe Hu and
Young-Ju Lee and
Jinchao Xu and
Chen-Song Zhang On Adaptive Eulerian--Lagrangian Method
for Linear Convection--Diffusion
Problems . . . . . . . . . . . . . . . . 90--114
Floraine Cordier and
Pierre Degond and
Anela Kumbaro Phase Appearance or Disappearance in
Two-Phase Flows . . . . . . . . . . . . 115--148
Jeremy Ovadia and
Qing Nie Numerical Methods for Two-Dimensional
Stem Cell Tissue Growth . . . . . . . . 149--175
Andrew R. Winters and
David A. Kopriva High-Order Local Time Stepping on Moving
DG Spectral Element Meshes . . . . . . . 176--202
Slimane Adjerid and
Idir Mechai A Superconvergent Discontinuous Galerkin
Method for Hyperbolic Problems on
Tetrahedral Meshes . . . . . . . . . . . 203--248
Ben-yu Guo and
Yu-jian Jiao Spectral Method for Navier--Stokes
Equations with Slip Boundary Conditions 249--274
Rongliang Chen and
Yuqi Wu and
Zhengzheng Yan and
Yubo Zhao and
Xiao-Chuan Cai A Parallel Domain Decomposition Method
for $3$D Unsteady Incompressible Flows
at High Reynolds Number . . . . . . . . 275--289
Andrew T. Barker and
Susanne C. Brenner A Mixed Finite Element Method for the
Stokes Equations Based on a Weakly
Over-Penalized Symmetric Interior
Penalty Approach . . . . . . . . . . . . 290--307
Zhimin Zhang and
Qingsong Zou A Family of Finite Volume Schemes of
Arbitrary Order on Rectangular Meshes 308--330
O. P. Bruno and
A. Prieto Spatially Dispersionless,
Unconditionally Stable FC--AD Solvers
for Variable-Coefficient PDEs . . . . . 331--366
Jun Hu and
Hongying Man and
Shangyou Zhang A Simple Conforming Mixed Finite Element
for Linear Elasticity on Rectangular
Grids in Any Space Dimension . . . . . . 367--379
Ruihan Guo and
Yan Xu Efficient Solvers of Discontinuous
Galerkin Discretization for the
Cahn--Hilliard Equations . . . . . . . . 380--408
J. Babbin and
P. A. Forsyth and
G. Labahn A Comparison of Iterated Optimal
Stopping and Local Policy Iteration for
American Options Under Regime Switching 409--430
Rongjie Lai and
Stanley Osher A Splitting Method for Orthogonality
Constrained Problems . . . . . . . . . . 431--449
Conghai Wu and
Ning Zhao A Stability Criterion for Semi-Discrete
Difference Schemes of Hyperbolic
Conservation Laws on Uniform Grids . . . 450--471
Roland Griesmaier and
Peter Monk Discretization of the Wave Equation
Using Continuous Elements in Time and a
Hybridizable Discontinuous Galerkin
Method in Space . . . . . . . . . . . . 472--498
Can Huang and
Zhimin Zhang Spectral Collocation Methods for
Differential-Algebraic Equations with
Arbitrary Index . . . . . . . . . . . . 499--516
Blanca Ayuso de Dios and
Franco Brezzi and
L. Donatella Marini and
Jinchao Xu and
Ludmil Zikatanov A Simple Preconditioner for a
Discontinuous Galerkin Method for the
Stokes Problem . . . . . . . . . . . . . 517--547
Qiyu Jin and
Ion Grama and
Quansheng Liu A New Poisson Noise Filter Based on
Weights Optimization . . . . . . . . . . 548--573
Jun Hu and
Yunqing Huang and
Quan Shen The Lower/Upper Bound Property of
Approximate Eigenvalues by Nonconforming
Finite Element Methods for Elliptic
Operators . . . . . . . . . . . . . . . 574--591
Alen Alexanderian and
Francesco Rizzi and
Muruhan Rathinam and
Olivier P. Le Ma\^\itre and
Omar M. Knio Preconditioned Bayesian Regression for
Stochastic Chemical Kinetics . . . . . . 592--626
Huadong Gao Optimal Error Analysis of Galerkin FEMs
for Nonlinear Joule Heating Equations 627--647
Dokkyun Yi An Iterative Scheme for Total
Variation-Based Image Denoising . . . . 648--671
Manuel Quezada de Luna and
David I. Ketcheson Numerical Simulation of Cylindrical
Solitary Waves in Periodic Media . . . . 672--689
Hanieh Mirzaee and
Jennifer K. Ryan and
Robert M. Kirby Smoothness-Increasing
Accuracy-Conserving (SIAC) Filters for
Discontinuous Galerkin Solutions:
Application to Structured Tetrahedral
Meshes . . . . . . . . . . . . . . . . . 690--704
Rongjie Lai and
Zaiwen Wen and
Wotao Yin and
Xianfeng Gu and
Lok Ming Lui Folding-Free Global Conformal Mapping
for Genus-$0$ Surfaces by Harmonic
Energy Minimization . . . . . . . . . . 705--725
John P. Boyd and
Rolfe Petschek The Relationships Between Chebyshev,
Legendre and Jacobi Polynomials: The
Generic Superiority of Chebyshev
Polynomials and Three Important
Exceptions . . . . . . . . . . . . . . . 1--27
Jacek Cyranka Efficient and Generic Algorithm for
Rigorous Integration Forward in Time of
dPDEs: Part I . . . . . . . . . . . . . 28--52
Xuying Zhao and
Zhong-Ci Shi and
Qiang Du Constraint-Free Adaptive FEMs on
Quadrilateral Nonconforming Meshes . . . 53--79
Ahad Zarghami and
Chiara Biscarini and
Sauro Succi and
Stefano Ubertini Hydrodynamics in Porous Media: a Finite
Volume Lattice Boltzmann Study . . . . . 80--103
Ya-nan Zhang and
Zhi-zhong Sun Error Analysis of a Compact ADI Scheme
for the $2$D Fractional Subdiffusion
Equation . . . . . . . . . . . . . . . . 104--128
Xiaobing Feng and
Thomas Lewis Local Discontinuous Galerkin Methods for
One-Dimensional Second Order Fully
Nonlinear Elliptic and Parabolic
Equations . . . . . . . . . . . . . . . 129--157
Tingchun Wang Optimal Point-Wise Error Estimate of a
Compact Difference Scheme for the
Coupled Gross--Pitaevskii Equations in
One Dimension . . . . . . . . . . . . . 158--186
Peng Chen and
Alfio Quarteroni and
Gianluigi Rozza Comparison Between Reduced Basis and
Stochastic Collocation Methods for
Elliptic Problems . . . . . . . . . . . 187--216
Fatih Celiker and
Li Fan HDG Methods for Naghdi Arches . . . . . 217--246
Björn Sjögreen and
N. Anders Petersson Source Estimation by Full Wave Form
Inversion . . . . . . . . . . . . . . . 247--276
Miyoun Jung and
Myeongmin Kang and
Myungjoo Kang Variational Image Segmentation Models
Involving Non-smooth Data-Fidelity Terms 277--308
Luke Owens Quasi-Optimal Convergence Rate of an
Adaptive Weakly Over-Penalized Interior
Penalty Method . . . . . . . . . . . . . 309--333
Jessica Meixner and
J. Casey Dietrich and
Clint Dawson and
Marcel Zijlema and
Leo H. Holthuijsen A Discontinuous Galerkin Coupled Wave
Propagation/Circulation Model . . . . . 334--370
George C. Hsiao and
Liwei Xu and
Shangyou Zhang Solving Negative Order Equations by the
Multigrid Method Via Variable
Substitution . . . . . . . . . . . . . . 371--385
Hayden Schaeffer and
Luminita Vese Variational Dynamics of Free Triple
Junctions . . . . . . . . . . . . . . . 386--411
Xiaofei Zhao and
Ziyi Li Numerical Methods and Simulations for
the Dynamics of One-Dimensional
Zakharov--Rubenchik Equations . . . . . 412--438
Ben-Yu Guo and
Xu-Hong Yu Composite Spectral Method for Exterior
Problems with Polygonal Obstacles . . . 439--472
Lin Mu and
Junping Wang and
Xiu Ye and
Shangyou Zhang A $ C^0 $-Weak Galerkin Finite Element
Method for the Biharmonic Equation . . . 473--495
Long Chen and
Junping Wang and
Xiu Ye A Posteriori Error Estimates for Weak
Galerkin Finite Element Methods for
Second Order Elliptic Problems . . . . . 496--511
Bernardo Cockburn and
Manuel Solano Solving Convection--Diffusion Problems
on Curved Domains by Extensions from
Subdomains . . . . . . . . . . . . . . . 512--543
Sébastien Leclaire and
Maud El-Hachem and
Jean-Yves Trépanier and
Marcelo Reggio High Order Spatial Generalization of
$2$D and $3$D Isotropic Discrete
Gradient Operators with Fast Evaluation
on GPUs . . . . . . . . . . . . . . . . 545--573
Wenbin Chen and
Cheng Wang and
Xiaoming Wang and
Steven M. Wise A Linear Iteration Algorithm for a
Second-Order Energy Stable Scheme for a
Thin Film Model Without Slope Selection 574--601
Thomas Lewis and
Michael Neilan Convergence Analysis of a Symmetric
Dual-Wind Discontinuous Galerkin Method 602--625
Sehun Chun Method of Moving Frames to Solve
(An)isotropic Diffusion Equations on
Curved Surfaces . . . . . . . . . . . . 626--666
Li-Lian Wang and
Xiaodan Zhao and
Zhimin Zhang Superconvergence of Jacobi--Gauss-Type
Spectral Interpolation . . . . . . . . . 667--687
Lulu Tian and
Yan Xu and
J. G. M. Kuerten and
J. J. W. Van der Vegt A Local Discontinuous Galerkin Method
for the Propagation of Phase Transition
in Solids and Fluids . . . . . . . . . . 688--720
D. M. Williams and
A. Jameson Energy Stable Flux Reconstruction
Schemes for Advection--Diffusion
Problems on Tetrahedra . . . . . . . . . 721--759
D. M. Williams and
A. Jameson Erratum to: Energy Stable Flux
Reconstruction Schemes for
Advection--Diffusion Problems on
Tetrahedra . . . . . . . . . . . . . . . 760--760
Zhicheng Hu and
Ruo Li and
Tiao Lu and
Yanli Wang and
Wenqi Yao Simulation of an $ n^+ \hbox {-}n \hbox
{-}n^+ $ Diode by Using
Globally-Hyperbolically-Closed
High-Order Moment Models . . . . . . . . 761--774
V. J. Ervin and
E. W. Jenkins and
Hyesuk Lee Approximation of the Stokes--Darcy
System by Optimization . . . . . . . . . 775--794
Mahboub Baccouch The Local Discontinuous Galerkin Method
for the Fourth-Order Euler--Bernoulli
Partial Differential Equation in One
Space Dimension. Part I:
Superconvergence Error Analysis . . . . 795--840
Mahboub Baccouch The Local Discontinuous Galerkin Method
for the Fourth-Order Euler--Bernoulli
Partial Differential Equation in One
Space Dimension. Part II: A Posteriori
Error Estimation . . . . . . . . . . . . 1--34
S. Götschel and
N. Chamakuri and
K. Kunisch and
M. Weiser Lossy Compression in Optimal Control of
Cardiac Defibrillation . . . . . . . . . 35--59
Wen-Ze Shao and
Hai-Song Deng and
Zhi-Hui Wei Kullback--Leibler Divergence Based
Composite Prior Modeling for Bayesian
Super-Resolution . . . . . . . . . . . . 60--78
Huibin Chang and
Xiaoqun Zhang and
Xue-Cheng Tai and
Danping Yang Domain Decomposition Methods for
Nonlocal Total Variation Image
Restoration . . . . . . . . . . . . . . 79--100
David C. Seal and
Yaman Güçlü and
Andrew J. Christlieb High-Order Multiderivative Time
Integrators for Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 101--140
Avram Sidi Richardson Extrapolation on Some Recent
Numerical Quadrature Formulas for
Singular and Hypersingular Integrals and
Its Study of Stability . . . . . . . . . 141--159
Ning Du and
Liang Ge and
Wenbin Liu Adaptive Finite Element Approximation
for an Elliptic Optimal Control Problem
with Both Pointwise and Integral Control
Constraints . . . . . . . . . . . . . . 160--183
B. Achchab and
A. Agouzal and
N. Debit and
K. Bouihat Star-Based a Posteriori Error Estimates
for Elliptic Problems . . . . . . . . . 184--202
Paola F. Antonietti and
Stefano Giani and
Paul Houston Domain Decomposition Preconditioners for
Discontinuous Galerkin Methods for
Elliptic Problems on Complicated Domains 203--227
Christopher B. Davis A Partition of Unity Method with Penalty
for Fourth Order Problems . . . . . . . 228--248
Tsz Ching Ng and
Xianfeng Gu and
Lok Ming Lui Computing Extremal Teichmüller Map of
Multiply-Connected Domains Via Beltrami
Holomorphic Flow . . . . . . . . . . . . 249--275
Xia Ji and
Jiguang Sun and
Hehu Xie A Multigrid Method for Helmholtz
Transmission Eigenvalue Problems . . . . 276--294
Tahar Z. Boulmezaoud and
Samy Mziou and
Tahar Boudjedaa Numerical Approximation of Second-Order
Elliptic Problems in Unbounded Domains 295--312
Ethan J. Kubatko and
Benjamin A. Yeager and
David I. Ketcheson Optimal Strong-Stability-Preserving
Runge--Kutta Time Discretizations for
Discontinuous Galerkin Methods . . . . . 313--344
Hillel Tal-Ezer Nonperiodic Trigonometric Polynomial
Approximation . . . . . . . . . . . . . 345--362
Manuel J. Castro and
José M. Gallardo and
Antonio Marquina A Class of Incomplete Riemann Solvers
Based on Uniform Rational Approximations
to the Absolute Value Function . . . . . 363--389
Jilu Wang A New Error Analysis of Crank--Nicolson
Galerkin FEMs for a Generalized
Nonlinear Schrödinger Equation . . . . . 390--407
E. D. Fernández-Nieto and
E. H. Koné and
T. Chacón Rebollo A Multilayer Method for the Hydrostatic
Navier--Stokes Equations: a Particular
Weak Solution . . . . . . . . . . . . . 408--437
Jochen Schütz An Asymptotic Preserving Method for
Linear Systems of Balance Laws Based on
Galerkin's Method . . . . . . . . . . . 438--456
James King and
Sergey Yakovlev and
Zhisong Fu and
Robert M. Kirby and
Spencer J. Sherwin Exploiting Batch Processing on Streaming
Architectures to Solve $2$D Elliptic
Finite Element Problems: A Hybridized
Discontinuous Galerkin (HDG) Case Study 457--482
Dai-Qiang Chen and
Yan Zhou Multiplicative Denoising Based on
Linearized Alternating Direction Method
Using Discrepancy Function Constraint 483--504
Simona Perotto and
Alessandro Veneziani Coupled Model and Grid Adaptivity in
Hierarchical Reduction of Elliptic
Problems . . . . . . . . . . . . . . . . 505--536
Francesco Ballarin and
Andrea Manzoni and
Gianluigi Rozza and
Sandro Salsa Shape Optimization by Free-Form
Deformation: Existence Results and
Numerical Solution for Stokes Flows . . 537--563
Yueqiang Shang and
Shumei Huang A Parallel Subgrid Stabilized Finite
Element Method Based on Two-Grid
Discretization for Simulation of
$2$D/$3$D Steady Incompressible Flows 564--583
Remi Abgrall and
Harish Kumar Robust Finite Volume Schemes for
Two-Fluid Plasma Equations . . . . . . . 584--611
Hans Johnston and
Cheng Wang and
Jian-Guo Liu A Local Pressure Boundary Condition
Spectral Collocation Scheme for the
Three-Dimensional Navier--Stokes
Equations . . . . . . . . . . . . . . . 612--626
R. D'Ambrosio and
E. Hairer Long-Term Stability of Multi-Value
Methods for Ordinary Differential
Equations . . . . . . . . . . . . . . . 627--640
F. Ar\`andiga and
M. C. Martí and
P. Mulet Weights Design For Maximal Order WENO
Schemes . . . . . . . . . . . . . . . . 641--659
Jianying Zhang and
Guangwu Yan Three-Dimensional Lattice Boltzmann
Model for the Complex Ginzburg--Landau
Equation . . . . . . . . . . . . . . . . 660--683
A. Y. Suhov An Accurate Polynomial Approximation of
Exponential Integrators . . . . . . . . 684--698
Li-Bin Liu and
Yanping Chen A Robust Adaptive Grid Method for a
System of Two Singularly Perturbed
Convection--Diffusion Equations with
Weak Coupling . . . . . . . . . . . . . 1--16
Yunhai Xiao and
Soon-Yi Wu and
Liqun Qi Nonmonotone Barzilai--Borwein Gradient
Algorithm for $ \ell_1$-Regularized
Nonsmooth Minimization in Compressive
Sensing . . . . . . . . . . . . . . . . 17--41
Yifan Zhang and
Wei Wang and
Johnny Guzmán and
Chi-Wang Shu Multi-scale Discontinuous Galerkin
Method for Solving Elliptic Problems
with Curvilinear Unidirectional Rough
Coefficients . . . . . . . . . . . . . . 42--60
Debojyoti Ghosh and
James D. Baeder Weighted Non-linear Compact Schemes for
the Direct Numerical Simulation of
Compressible, Turbulent Flows . . . . . 61--89
Kristoffer Virta and
Ken Mattsson Acoustic Wave Propagation in Complicated
Geometries and Heterogeneous Media . . . 90--118
Hong Zhang and
Adrian Sandu and
Sebastien Blaise Partitioned and Implicit--Explicit
General Linear Methods for Ordinary
Differential Equations . . . . . . . . . 119--144
M. Bebendorf and
C. Kuske Separation of Variables for Function
Generated High-Order Tensors . . . . . . 145--165
Dimitrios Mitsotakis and
Boaz Ilan and
Denys Dutykh On the Galerkin/Finite-Element Method
for the Serre Equations . . . . . . . . 166--195
Jun Hu and
Yunqing Huang and
Qun Lin Lower Bounds for Eigenvalues of Elliptic
Operators: By Nonconforming Finite
Element Methods . . . . . . . . . . . . 196--221
Xuguang Yang and
Baochang Shi and
Zhenhua Chai and
Zhaoli Guo A Coupled Lattice Boltzmann Method to
Solve Nernst--Planck Model for
Simulating Electro-osmotic Flows . . . . 222--238
Luisa D'Amore and
Rossella Arcucci and
Luisa Carracciuolo and
Almerico Murli A Scalable Approach for Variational Data
Assimilation . . . . . . . . . . . . . . 239--257
Haijian Yang and
Chao Yang and
Xiao-Chuan Cai Parallel Domain Decomposition Methods
with Mixed Order Discretization for
Fully Implicit Solution of Tracer
Transport Problems on the Cubed-Sphere 258--280
Lei Shi and
Z. J. Wang and
L. P. Zhang and
Wei Liu and
Song Fu A $ P_N P_M$-CPR Framework for
Hyperbolic Conservation Laws . . . . . . 281--307
Qianhuan Li and
Zhenhua Chai and
Baochang Shi An Efficient Lattice Boltzmann Model for
Steady Convection--Diffusion Equation 308--326
Adrian Sescu and
Ray Hixon Numerical Anisotropy Study of a Class of
Compact Schemes . . . . . . . . . . . . 327--342
Pawel Buchmüller and
Christiane Helzel Improved Accuracy of High-Order WENO
Finite Volume Methods on Cartesian Grids 343--368
Martin Almquist and
Ilkka Karasalo and
Ken Mattsson Atmospheric Sound Propagation Over
Large-Scale Irregular Terrain . . . . . 369--397
F. D. Witherden and
P. E. Vincent An Analysis of Solution Point
Coordinates for Flux Reconstruction
Schemes on Triangular Elements . . . . . 398--423
Uwe Köcher and
Markus Bause Variational Space--Time Methods for the
Wave Equation . . . . . . . . . . . . . 424--453
B. Pincock and
A. Katz High-Order Flux Correction for Viscous
Flows on Arbitrary Unstructured Grids 454--476
Alessandro De Rosis and
Stefano Ubertini and
Francesco Ubertini A Comparison Between the Interpolated
Bounce-Back Scheme and the Immersed
Boundary Method to Treat Solid Boundary
Conditions for Laminar Flows in the
Lattice Boltzmann Framework . . . . . . 477--489
Adam Martinez and
Anne Gelb and
Alexander Gutierrez Edge Detection from Non-Uniform Fourier
Data Using the Convolutional Gridding
Algorithm . . . . . . . . . . . . . . . 490--512
A. Roth and
A. Klar and
B. Simeon and
E. Zharovsky A Semi-Lagrangian Method for $3$-D
Fokker Planck Equations for Stochastic
Dynamical Systems on the Sphere . . . . 513--532
Haifeng Ji and
Jinru Chen and
Zhilin Li A Symmetric and Consistent Immersed
Finite Element Method for Interface
Problems . . . . . . . . . . . . . . . . 533--557
Wei-Qiang Huang and
Xianfeng David Gu and
Wen-Wei Lin and
Shing-Tung Yau A Novel Symmetric Skew-Hamiltonian
Isotropic Lanczos Algorithm for Spectral
Conformal Parameterizations . . . . . . 558--583
Yinhua Xia Fourier Spectral Methods for
Degasperis--Procesi Equation with
Discontinuous Solutions . . . . . . . . 584--603
André Massing and
Mats G. Larson and
Anders Logg and
Marie E. Rognes A Stabilized Nitsche Fictitious Domain
Method for the Stokes Problem . . . . . 604--628
Hong-lin Liao and
Ya-nan Zhang and
Ying Zhao and
Han-sheng Shi Stability and Convergence of Modified Du
Fort--Frankel Schemes for Solving
Time-Fractional Subdiffusion Equations 629--648
David P. Starinshak and
Smadar Karni and
Philip L. Roe A New Level-Set Model for the
Representation of Non-Smooth Geometries 649--672
Xu-Hong Yu and
Ben-Yu Guo Spectral Element Method for Mixed
Inhomogeneous Boundary Value Problems of
Fourth Order . . . . . . . . . . . . . . 673--701
Youngjoon Hong Numerical Approximation of the
Singularly Perturbed Heat Equation in a
Circle . . . . . . . . . . . . . . . . . 1--24
Nils Gerhard and
Francesca Iacono and
Georg May and
Siegfried Müller and
Roland Schäfer A High-Order Discontinuous Galerkin
Discretization with Multiwavelet-Based
Grid Adaptation for Compressible Flows 25--52
D. Shirokoff and
J.-C. Nave A Sharp-Interface Active Penalty Method
for the Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 53--77
Bernard Bialecki and
Andreas Karageorghis Finite Difference Schemes for the
Cauchy--Navier Equations of Elasticity
with Variable Coefficients . . . . . . . 78--121
Yunqing Huang and
Jichun Li and
Chao Wu and
Wei Yang Superconvergence Analysis for Linear
Tetrahedral Edge Elements . . . . . . . 122--145
Da Xu Decay Properties for the Numerical
Solutions of a Partial Differential
Equation with Memory . . . . . . . . . . 146--178
Chunmei Wang and
Shangyou Zhang and
Jinru Chen A Unified Mortar Condition for
Nonconforming Finite Elements . . . . . 179--197
Liang Wu and
Yong-Tao Zhang A Third Order Fast Sweeping Method with
Linear Computational Complexity for
Eikonal Equations . . . . . . . . . . . 198--229
Yinnian He and
Pengzhan Huang and
Xinlong Feng $ H^2 $-Stability of the First Order
Fully Discrete Schemes for the
Time-Dependent Navier--Stokes Equations 230--264
B. Bialecki and
G. Fairweather and
J. C. López-Marcos The Extrapolated Crank--Nicolson
Orthogonal Spline Collocation Method for
a Quasilinear Parabolic Problem with
Nonlocal Boundary Conditions . . . . . . 265--283
Yidu Yang and
Jiayu Han and
Hai Bi and
Yuanyuan Yu The Lower/Upper Bound Property of the
Crouzeix--Raviart Element Eigenvalues on
Adaptive Meshes . . . . . . . . . . . . 284--299
Ming Li and
Yujiao Wang and
Leevan Ling Numerical Caputo Differentiation by
Radial Basis Functions . . . . . . . . . 300--315
Ruo Li and
Tiao Lu and
Wenqi Yao Discrete Kernel Preserving Model for
$1$D Electron--Optical Phonon Scattering 317--335
Miyoun Jung and
Myungjoo Kang Efficient Nonsmooth Nonconvex
Optimization for Image Restoration and
Segmentation . . . . . . . . . . . . . . 336--370
Christophe Buet and
Bruno Després and
Emmanuel Franck Asymptotic Preserving Schemes on
Distorted Meshes for Friedrichs Systems
with Stiff Relaxation: Application to
Angular Models in Linear Transport . . . 371--398
Mahboub Baccouch and
Slimane Adjerid A Posteriori Local Discontinuous
Galerkin Error Estimation for
Two-Dimensional Convection--Diffusion
Problems . . . . . . . . . . . . . . . . 399--430
Lili Ju and
Jian Zhang and
Liyong Zhu and
Qiang Du Fast Explicit Integration Factor Methods
for Semilinear Parabolic Equations . . . 431--455
Michael Hintermüller and
Andreas Langer Non-Overlapping Domain Decomposition
Methods For Dual Total Variation Based
Image Denoising . . . . . . . . . . . . 456--481
C. H. Yu and
Yogesh G. Bhumkar and
Tony W. H. Sheu Dispersion Relation Preserving Combined
Compact Difference Schemes for Flow
Problems . . . . . . . . . . . . . . . . 482--516
Andrew Skelton and
Allan R. Willms Parameter Range Reduction in Ordinary
Differential Equation Models . . . . . . 517--531
Matthew A. Reyna and
Fengyan Li Operator Bounds and Time Step Conditions
for the DG and Central DG Methods . . . 532--554
Jingwei Hu and
Qin Li and
Lorenzo Pareschi Asymptotic-Preserving Exponential
Methods for the Quantum Boltzmann
Equation with High-Order Accuracy . . . 555--574
Feng Chen A New Framework of GPU-Accelerated
Spectral Solvers: Collocation and
Glerkin Methods for Systems of Coupled
Elliptic Equations . . . . . . . . . . . 575--600
Chun Liu and
Jie Shen and
Xiaofeng Yang Decoupled Energy Stable Schemes for a
Phase-Field Model of Two-Phase
Incompressible Flows with Variable
Density . . . . . . . . . . . . . . . . 601--622
Mohamed Addam and
Abderrahman Bouhamidi and
Mohammed Seaid A Frequency-Domain Approach for the $
P_1 $ Approximation of Time-Dependent
Radiative Transfer . . . . . . . . . . . 623--651
Xudong Yao Convergence Analysis of a Minimax Method
for Finding Multiple Solutions of
Semilinear Elliptic Equation: Part I ---
On Polyhedral Domain . . . . . . . . . . 652--673
Guoliang Xu and
Qing Pan Design of Loop's Subdivision Surfaces by
Fourth-Order Geometric PDEs with $ G^1 $
Boundary Conditions . . . . . . . . . . 674--692
V. M. Ashwin and
K. Saurabh and
M. Sriramkrishnan and
P. M. Bagade and
M. K. Parvathi and
Tapan K. Sengupta KdV Equation and Computations of
Solitons: Nonlinear Error Dynamics . . . 693--717
Weihua Deng and
Minghua Chen and
Eli Barkai Numerical Algorithms for the Forward and
Backward Fractional Feynman--Kac
Equations . . . . . . . . . . . . . . . 718--746
Xuan Zhao and
Zhi-Zhong Sun Compact Crank--Nicolson Schemes for a
Class of Fractional Cattaneo Equation in
Inhomogeneous Medium . . . . . . . . . . 747--771
Andrzej Warzy\'nski and
Matthew E. Hubbard and
Mario Ricchiuto Runge--Kutta Residual Distribution
Schemes . . . . . . . . . . . . . . . . 772--802
Hailiang Liu and
Hui Yu The Entropy Satisfying Discontinuous
Galerkin Method for Fokker--Planck
equations . . . . . . . . . . . . . . . 803--830
T. Ohtsuka and
Y.-H. R. Tsai and
Y. Giga A Level Set Approach Reflecting Sheet
Structure with Single Auxiliary Function
for Evolving Spirals on Crystal Surfaces 831--874
Florencia Parisi and
Mariana Cécere and
Mirta Iriondo and
Oscar Reula Numerical Treatment of Interfaces for
Second-Order Wave Equations . . . . . . 875--897
Guido Ala and
Elisa Francomano Numerical Investigations of an Implicit
Leapfrog Time-Domain Meshless Method . . 898--912
Kartikey Asthana and
Antony Jameson High-Order Flux Reconstruction Schemes
with Minimal Dispersion and Dissipation 913--944
Can Huang and
Zhimin Zhang On the Spectrum Computation of
Non-oscillatory and Highly Oscillatory
Kernel with Weak Singularity . . . . . . 1--22
Martin L. Sætra and
André R. Brodtkorb and
Knut-Andreas Lie Efficient GPU-Implementation of Adaptive
Mesh Refinement for the Shallow-Water
Equations . . . . . . . . . . . . . . . 23--48
Feilin Jia and
Zhen Gao and
Wai Sun Don A Spectral Study on the Dissipation and
Dispersion of the WENO Schemes . . . . . 49--77
John W. Barrett and
Harald Garcke and
Robert Nürnberg A Stable Parametric Finite Element
Discretization of Two-Phase
Navier--Stokes Flow . . . . . . . . . . 78--117
Shan Zhao A Matched Alternating Direction Implicit
(ADI) Method for Solving the Heat
Equation with Interfaces . . . . . . . . 118--137
Lucas C. Wilcox and
Georg Stadler and
Tan Bui-Thanh and
Omar Ghattas Discretely Exact Derivatives for
Hyperbolic PDE-Constrained Optimization
Problems Discretized by the
Discontinuous Galerkin Method . . . . . 138--162
Fermín S. Viloche Bazán Simple and Efficient Determination of
the Tikhonov Regularization Parameter
Chosen by the Generalized Discrepancy
Principle for Discrete Ill--Posed
Problems . . . . . . . . . . . . . . . . 163--184
James C. Hateley and
Huayi Wei and
Long Chen Fast Methods for Computing Centroidal
Voronoi Tessellations . . . . . . . . . 185--212
Seungmi Oh and
Myungjoo Kang Image Decomposition using a Local
Gradient Constraint . . . . . . . . . . 213--232
Suncica Canic and
Benedetto Piccoli and
Jing-Mei Qiu and
Tan Ren Runge--Kutta Discontinuous Galerkin
Method for Traffic Flow Model on
Networks . . . . . . . . . . . . . . . . 233--255
J. Rocha de Faria and
D. Lesnic Topological Derivative for the Inverse
Conductivity Problem: a Bayesian
Approach . . . . . . . . . . . . . . . . 256--278
Matt Elsey and
Benedikt Wirth Redistancing Dynamics for Vector--Valued
Multilabel Segmentation with Costly
Fidelity: Grain Identification in
Polycrystal Images . . . . . . . . . . . 279--306
Yuhui Quan and
Hui Ji and
Zuowei Shen Data-Driven Multi-scale Non-local
Wavelet Frame Construction and Image
Recovery . . . . . . . . . . . . . . . . 307--329
Maxime Theillard and
Frédéric Gibou and
Tresa Pollock A Sharp Computational Method for the
Simulation of the Solidification of
Binary Alloys . . . . . . . . . . . . . 330--354
Chang-Yeol Jung and
Thien Binh Nguyen Semi-analytical Time Differencing
Methods for Stiff Problems . . . . . . . 355--373
Linda Stals Efficient Solution Techniques for a
Finite Element Thin Plate Spline
Formulation . . . . . . . . . . . . . . 374--409
Jun Hu and
Rui Ma The Enriched Crouzeix--Raviart Elements
are Equivalent to the Raviart--Thomas
Elements . . . . . . . . . . . . . . . . 410--425
Xiaojing Dong and
Yinnian He Two-Level Newton Iterative Method for
the 2$D$ /3$D$ Stationary Incompressible
Magnetohydrodynamics . . . . . . . . . . 426--451
Yao Cheng and
Feng Zhang and
Qiang Zhang Local Analysis of Local Discontinuous
Galerkin Method for the Time-Dependent
Singularly Perturbed Problem . . . . . . 452--477
Faker Ben Belgacem and
Christine Bernardi and
Faten Jelassi and
Maimouna Mint Brahim Finite Element Methods for the
Temperature in Composite Media with
Contact Resistance . . . . . . . . . . . 478--501
L. Arpaia and
M. Ricchiuto and
R. Abgrall An ALE Formulation for Explicit
Runge--Kutta Residual Distribution . . . 502--547
Hongxia Liu and
Jianxian Qiu Finite Difference Hermite WENO Schemes
for Hyperbolic Conservation Laws . . . . 548--572
Lok Ming Lui and
Tsz Ching Ng A Splitting Method for Diffeomorphism
Optimization Problem Using Beltrami
Coefficients . . . . . . . . . . . . . . 573--611
Akmal Nizam Mohammed and
Farzad Ismail Entropy Consistent Methods for the
Navier--Stokes Equations . . . . . . . . 612--631
Willem Hundsdorfer and
David I. Ketcheson and
Igor Savostianov Error Analysis of Explicit Partitioned
Runge--Kutta Schemes for Conservation
Laws . . . . . . . . . . . . . . . . . . 633--653
Roberto Natalini and
Magali Ribot and
Monika Twarogowska A Numerical Comparison Between
Degenerate Parabolic and Quasilinear
Hyperbolic Models of Cell Movements
Under Chemotaxis . . . . . . . . . . . . 654--677
Suo Yang and
Alexander Kurganov and
Yingjie Liu Well-Balanced Central Schemes on
Overlapping Cells with Constant
Subtraction Techniques for the
Saint-Venant Shallow Water System . . . 678--698
Min Yang and
Jiangguo Liu and
Yanping Lin Pressure Recovery for Weakly
Over--Penalized Discontinuous Galerkin
Methods for the Stokes Problem . . . . . 699--715
Long Chen and
Ming Wang and
Lin Zhong Convergence Analysis of Triangular MAC
Schemes for Two Dimensional Stokes
Equations . . . . . . . . . . . . . . . 716--744
Varun Shankar and
Grady B. Wright and
Robert M. Kirby and
Aaron L. Fogelson A Radial Basis Function (RBF)-Finite
Difference (FD) Method for Diffusion and
Reaction--Diffusion Equations on
Surfaces . . . . . . . . . . . . . . . . 745--768
Claudio Canuto and
Valeria Simoncini and
Marco Verani Contraction and Optimality Properties of
an Adaptive Legendre--Galerkin Method:
The Multi-Dimensional Case . . . . . . . 769--798
Tasos Rossides and
David J. B. Lloyd and
Sergey Zelik Computing Interacting Multi-fronts in
One Dimensional Real Ginzburg Landau
Equations . . . . . . . . . . . . . . . 799--819
Hél\`ene Mathis and
Clément Canc\`es and
Edwige Godlewski and
Nicolas Seguin Dynamic Model Adaptation for Multiscale
Simulation of Hyperbolic Systems with
Relaxation . . . . . . . . . . . . . . . 820--861
Shengxin Zhu and
Andrew J. Wathen Convexity and Solvability for Compactly
Supported Radial Basis Functions with
Different Shapes . . . . . . . . . . . . 862--884
T. Chacón Rebollo and
M. Gómez Mármol and
M. Restelli Numerical Analysis of Penalty Stabilized
Finite Element Discretizations of
Evolution Navier--Stokes Equations . . . 885--912
Ruihan Guo and
Yan Xu and
Zhengfu Xu Local Discontinuous Galerkin Methods for
the Functionalized Cahn--Hilliard
Equation . . . . . . . . . . . . . . . . 913--937
Vít Dolejsí and
Ivana Sebestová and
Martin Vohralík Algebraic and Discretization Error
Estimation by Equilibrated Fluxes for
Discontinuous Galerkin Methods on
Nonmatching Grids . . . . . . . . . . . 1--34
Jen-Hao Chen and
I-Liang Chern and
Weichung Wang A Complete Study of the Ground State
Phase Diagrams of Spin-1 Bose--Einstein
Condensates in a Magnetic Field Via
Continuation Methods . . . . . . . . . . 35--54
Rikhi Bose and
Tapan K. Sengupta Analysis and Design of a New Dispersion
Relation Preserving Alternate Direction
Bidiagonal Compact Scheme . . . . . . . 55--82
Tiexiang Li and
Wei-Qiang Huang and
Wen-Wei Lin and
Jijun Liu On Spectral Analysis and a Novel
Algorithm for Transmission Eigenvalue
Problems . . . . . . . . . . . . . . . . 83--108
Changchun Wang and
Jianxin Zhou A New Approach for Numerically Solving
Nonlinear Eigensolution Problems . . . . 109--129
Yanli Chen and
Yonghai Li and
Zhiqiang Sheng and
Guangwei Yuan Adaptive Bilinear Element Finite Volume
Methods for Second-Order Elliptic
Problems on Nonmatching Grids . . . . . 130--150
John C. Bowman and
Mohammad Ali Yassaei and
Anup Basu A Fully Lagrangian Advection Scheme . . 151--177
Yifei Lou and
Penghang Yin and
Qi He and
Jack Xin Computing Sparse Representation in a
Highly Coherent Dictionary Based on
Difference of $ L_1 $ and $ L_2 $ . . . 178--196
Yao Sun and
Fuming Ma and
Xu Zhou An Invariant Method of Fundamental
Solutions for the Cauchy Problem in
Two-Dimensional Isotropic Linear
Elasticity . . . . . . . . . . . . . . . 197--215
Abner J. Salgado Convergence Analysis of Fractional
Time-Stepping Techniques for
Incompressible Fluids with
Microstructure . . . . . . . . . . . . . 216--233
Xiaojie Wang An Exponential Integrator Scheme for
Time Discretization of Nonlinear
Stochastic Wave Equation . . . . . . . . 234--263
Nan Jiang A Higher Order Ensemble Simulation
Algorithm for Fluid Flows . . . . . . . 264--288
Po-Wen Hsieh and
Ming-Chih Lai and
Suh-Yuh Yang and
Cheng-Shu You An Unconditionally Energy Stable Penalty
Immersed Boundary Method for Simulating
the Dynamics of an Inextensible
Interface Interacting with a Solid
Particle . . . . . . . . . . . . . . . . 289--316
Min Zhong and
Yiu Chung Hon and
Shuai Lu Multiscale Support Vector Approach for
Solving Ill-Posed Problems . . . . . . . 317--340
Ali Safdari-Vaighani and
Alfa Heryudono and
Elisabeth Larsson A Radial Basis Function Partition of
Unity Collocation Method for
Convection--Diffusion Equations Arising
in Financial Applications . . . . . . . 341--367
Jikun Zhao and
Shaochun Chen and
Bei Zhang and
Shipeng Mao Robust a Posteriori Error Estimates for
Conforming Discretizations of Diffusion
Problems with Discontinuous Coefficients
on Anisotropic Meshes . . . . . . . . . 368--400
Paulo Rafael Bösing and
Carsten Carstensen Discontinuous Galerkin with Weakly
Over-Penalized Techniques for
Reissner--Mindlin Plates . . . . . . . . 401--424
Gonzalo Rubio and
François Fraysse and
David A. Kopriva and
Eusebio Valero Quasi-A Priori Truncation Error
Estimation in the DGSEM . . . . . . . . 425--455
Hailong Guo and
Zhimin Zhang Gradient Recovery for the
Crouzeix--Raviart Element . . . . . . . 456--476
Chieh-Sen Huang and
Feng Xiao and
Todd Arbogast Fifth Order Multi-moment WENO Schemes
for Hyperbolic Conservation Laws . . . . 477--507
Youngmok Jeon Hybrid Difference Methods for PDEs . . . 508--521
Jochen Schütz and
Sebastian Noelle Flux Splitting for Stiff Equations: a
Notion on Stability . . . . . . . . . . 522--540
A. Linke and
C. Merdon Guaranteed Energy Error Estimators for a
Modified Robust Crouzeix--Raviart Stokes
Element . . . . . . . . . . . . . . . . 541--558
Ran Zhang and
Qilong Zhai A Weak Galerkin Finite Element Scheme
for the Biharmonic Equations by Using
Polynomials of Reduced Order . . . . . . 559--585
Jan S. Hesthaven and
Jae-Hun Jung and
Allen Tesdall Hyperbolic Problems: Theory and
Computation . . . . . . . . . . . . . . 587--590
Weitao Chen and
Ching-Shan Chou and
Chiu-Yen Kao Lax--Friedrichs Multigrid Fast Sweeping
Methods for Steady State Problems for
Hyperbolic Conservation Laws . . . . . . 591--618
Weitao Chen and
Ching-Shan Chou and
Chiu-Yen Kao Erratum to: Lax--Friedrichs Multigrid
Fast Sweeping Methods for Steady State
Problems for Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 619--619
X. Antoine and
E. Lorin and
A. D. Bandrauk Domain Decomposition Method and
High-Order Absorbing Boundary Conditions
for the Numerical Simulation of the Time
Dependent Schrödinger Equation with
Ionization and Recombination by Intense
Electric Field . . . . . . . . . . . . . 620--646
Scott E. Field and
Stephen R. Lau Fast Evaluation of Far-Field Signals for
Time-Domain Wave Propagation . . . . . . 647--669
Peng Li and
Zhen Gao and
Wai-Sun Don and
Shusen Xie Hybrid Fourier-Continuation Method and
Weighted Essentially Non-oscillatory
Finite Difference Scheme for Hyperbolic
Conservation Laws in a Single-Domain
Framework . . . . . . . . . . . . . . . 670--695
Xuefeng Li and
Katarzyna Saxton Non-strictly Hyperbolic Systems,
Singularity and Bifurcation . . . . . . 696--720
Allen M. Tesdall and
Richard Sanders and
Nedyu Popivanov Further Results on Guderley Mach
Reflection and the Triple Point Paradox 721--744
Junxiong Jia and
Ronghua Pan On Isentropic Approximations for
Compressible Euler Equations . . . . . . 745--760
Blake Temple and
Robin Young A Nash--Moser Framework for Finding
Periodic Solutions of the Compressible
Euler Equations . . . . . . . . . . . . 761--772
Jennifer K. Ryan and
Xiaozhou Li and
Robert M. Kirby and
Kees Vuik One-Sided Position-Dependent
Smoothness-Increasing
Accuracy-Conserving (SIAC) Filtering
Over Uniform and Non-uniform Meshes . . 773--817
D. Cho\"\i and
L. Gallimard and
T. Sassi A Posteriori Estimates for a Natural
Neumann--Neumann Domain Decomposition
Algorithm on a Unilateral Contact
Problem . . . . . . . . . . . . . . . . 818--836
Chiu-Yen Kao and
Alexander Kurganov and
Zhuolin Qu and
Ying Wang A Fast Explicit Operator Splitting
Method for Modified Buckley--Leverett
Equations . . . . . . . . . . . . . . . 837--857
R. Das and
P. W. Cleary Evaluation of Accuracy and Stability of
the Classical SPH Method Under Uniaxial
Compression . . . . . . . . . . . . . . 858--897
Navnit Jha and
Leslaw K. Bieniasz A Fifth (Six) Order Accurate,
Three--Point Compact Finite Difference
Scheme for the Numerical Solution of
Sixth Order Boundary Value Problems on
Geometric Meshes . . . . . . . . . . . . 898--913
Youqiong Liu and
Jianhu Feng and
Jiong Ren High Resolution, Entropy--Consistent
Scheme Using Flux Limiter for Hyperbolic
Systems of Conservation Laws . . . . . . 914--937
J. I. Montijano and
L. Rández and
M. Van Daele and
M. Calvo Functionally Fitted Explicit Two Step
Peer Methods . . . . . . . . . . . . . . 938--958
Cui-cui Ji and
Zhi-zhong Sun A High-Order Compact Finite Difference
Scheme for the Fractional Sub-diffusion
Equation . . . . . . . . . . . . . . . . 959--985
Wanfang Shen and
Liang Ge and
Danping Yang and
Wenbin Liu Sharp A Posteriori Error Estimates for
Optimal Control Governed by Parabolic
Integro--Differential Equations . . . . 1--33
A. Lemoine and
J.-P. Caltagirone and
M. Aza\"\iez and
S. Vincent Discrete Helmholtz--Hodge Decomposition
on Polyhedral Meshes Using Compatible
Discrete Operators . . . . . . . . . . . 34--53
Martin Campos Pinto Towards Smooth Particle Methods Without
Smoothing . . . . . . . . . . . . . . . 54--82
Yan Guo and
Tao Xiong and
Yufeng Shi A Maximum--Principle-Satisfying
High-Order Finite Volume Compact WENO
Scheme for Scalar Conservation Laws with
Applications in Incompressible Flows . . 83--109
Kwangil Kim and
Yonghai Li Construction of Convergent High Order
Schemes for Time Dependent
Hamilton--Jacobi Equations . . . . . . . 110--137
Shaohong Du and
Zhimin Zhang A Robust Residual-Type a Posteriori
Error Estimator for
Convection--Diffusion Equations . . . . 138--170
Muriel Boulakia and
Alexandre Genadot and
Mich\`ele Thieullen Simulation of SPDEs for Excitable Media
Using Finite Elements . . . . . . . . . 171--195
Hongling Su and
Shengtai Li Structure-Preserving Numerical Methods
for Infinite-Dimensional Birkhoffian
Systems . . . . . . . . . . . . . . . . 196--223
Tapan K. Sengupta and
V. K. Sathyanarayanan Role of Time Integration in Computing
Transitional Flows Caused by Wall
Excitation . . . . . . . . . . . . . . . 224--248
Paolo Gatto and
Jan S. Hesthaven Numerical Approximation of the
Fractional Laplacian via $ h p$-finite
Elements, with an Application to Image
Denoising . . . . . . . . . . . . . . . 249--270
Giuseppe Izzo and
Zdzis\law Jackiewicz Strong Stability Preserving General
Linear Methods . . . . . . . . . . . . . 271--298
Wei Guo and
Jing-Mei Qiu and
Jianxian Qiu A New Lax--Wendroff Discontinuous
Galerkin Method with Superconvergence 299--326
Issei Oikawa A Hybridized Discontinuous Galerkin
Method with Reduced Stabilization . . . 327--340
Jichun Li and
Shuyu Sun The Superconvergence Phenomenon and
Proof of the MAC Scheme for the Stokes
Equations on Non-uniform Rectangular
Meshes . . . . . . . . . . . . . . . . . 341--362
Lin Mu and
Junping Wang and
Xiu Ye and
Shangyou Zhang A Weak Galerkin Finite Element Method
for the Maxwell Equations . . . . . . . 363--386
J. Dölz and
H. Harbrecht and
M. Peters $ \mathcal {H} $-matrix Accelerated
Second Moment Analysis for Potentials
with Rough Correlation . . . . . . . . . 387--410
Fanhai Zeng Second-Order Stable Finite Difference
Schemes for the Time-Fractional
Diffusion-Wave Equation . . . . . . . . 411--430
Ki-Hong Kim and
Min-cheol Gwak and
Jack J. Yoh An Enhanced Particle Reseeding Algorithm
for the Hybrid Particle Level Set Method
in Compressible Flows . . . . . . . . . 431--453
Zhimin Zhang How Many Numerical Eigenvalues Can We
Trust? . . . . . . . . . . . . . . . . . 455--466
Jeng-Tzong Chen and
Yu-Lung Chang and
Shing-Kai Kao and
Jie Jian Revisit of the Indirect Boundary Element
Method: Necessary and Sufficient
Formulation . . . . . . . . . . . . . . 467--485
Anna Nissen and
Katharina Kormann and
Magnus Grandin and
Kristoffer Virta Stable Difference Methods for
Block-Oriented Adaptive Grids . . . . . 486--511
Haibiao Zheng and
Jiaping Yu and
Feng Shi Local and Parallel Finite Element
Algorithm Based on the Partition of
Unity for Incompressible Flows . . . . . 512--532
Gabriel Wasserman and
Rick Archibald and
Anne Gelb Image Reconstruction from Fourier Data
Using Sparsity of Edges . . . . . . . . 533--552
Rui Wang and
Xiangling Chen A Fast Solver for Boundary Integral
Equations of the Modified Helmholtz
Equation . . . . . . . . . . . . . . . . 553--575
Youngsoo Choi and
Charbel Farhat and
Walter Murray and
Michael Saunders A Practical Factorization of a Schur
Complement for PDE-Constrained
Distributed Optimal Control . . . . . . 576--597
Johnny Guzmán and
Manuel A. Sánchez Max-Norm Stability of Low Order
Taylor--Hood Elements in Three
Dimensions . . . . . . . . . . . . . . . 598--621
Li Guo and
Yan Xu Energy Conserving Local Discontinuous
Galerkin Methods for the Nonlinear
Schrödinger Equation with Wave Operator 622--647
Ben-yu Guo and
Chao Zhang Generalized Hermite Spectral Method
Matching Different Algebraic Decay at
infinities . . . . . . . . . . . . . . . 648--671
Christine Bernardi and
Jad Dakroub and
Gihane Mansour and
Toni Sayah A posteriori analysis of iterative
algorithms for a nonlinear problem . . . 672--697
M. Caliari and
S. Zuccher The Inverse Power Method for the $ p(x)
$-Laplacian Problem . . . . . . . . . . 698--714
Lijun Yi An $h$-$p$ Version of the Continuous
Petrov--Galerkin Finite Element Method
for Nonlinear Volterra
Integro-Differential Equations . . . . . 715--734
Florian Bernard and
Angelo Iollo and
Gabriella Puppo Accurate Asymptotic Preserving Boundary
Conditions for Kinetic Equations on
Cartesian Grids . . . . . . . . . . . . 735--766
Michiel E. Hochstenbach and
Lothar Reichel and
Xuebo Yu A Golub--Kahan-Type Reduction Method for
Matrix Pairs . . . . . . . . . . . . . . 767--789
Zhen-sheng Sun and
Yu-xin Ren and
Bai-lin Zha and
Shi-ying Zhang High Order Boundary Conditions for High
Order Finite Difference Schemes on
Curvilinear Coordinates Solving
Compressible Flows . . . . . . . . . . . 790--820
Julius Reiss A Family of Energy Stable,
Skew-Symmetric Finite Difference Schemes
on Collocated Grids . . . . . . . . . . 821--838
Sheng-Gwo Chen and
Mei-Hsiu Chi and
Jyh-Yang Wu High-Order Algorithms for
Laplace--Beltrami Operators and
Geometric Invariants over Curved
Surfaces . . . . . . . . . . . . . . . . 839--865
I. Magdalena and
N. Erwina and
S. R. Pudjaprasetya Staggered Momentum Conservative Scheme
For Radial Dam Break Simulation . . . . 867--874
Tao Lin and
Qing Yang and
Xu Zhang A Priori Error Estimates for Some
Discontinuous Galerkin Immersed Finite
Element Methods . . . . . . . . . . . . 875--894
Federica Porta and
Marco Prato and
Luca Zanni A New Steplength Selection for Scaled
Gradient Methods with Application to
Image Deblurring . . . . . . . . . . . . 895--919
Guo-Dong Zhang and
Yan Zhang and
Yinnian He Two-Level Coupled and Decoupled Parallel
Correction Methods for Stationary
Incompressible Magnetohydrodynamics . . 920--939
Hirofumi Notsu and
Masahisa Tabata Error Estimates of a Pressure-Stabilized
Characteristics Finite Element Scheme
for the Oseen Equations . . . . . . . . 940--955
Sarvesh Kumar and
Ricardo Ruiz-Baier Equal Order Discontinuous Finite Volume
Element Methods for the Stokes Problem 956--978
Mohan K. Kadalbajoo and
Lok Pati Tripathi and
Alpesh Kumar Second Order Accurate IMEX Methods for
Option Pricing Under Merton and Kou
Jump-Diffusion Models . . . . . . . . . 979--1024
Dong-yang Shi and
Ming-hao Li and
Chao Xu A New Stabilization Method for the
Elasticity Problem . . . . . . . . . . . 1025--1038
Monique Dauge and
Alexander Düster and
Ernst Rank Theoretical and Numerical Investigation
of the Finite Cell Method . . . . . . . 1039--1064
Pui Tung Choi and
Lok Ming Lui Fast Disk Conformal Parameterization of
Simply--Connected Open Surfaces . . . . 1065--1090
Nicolas Crouseilles and
Matthieu Kuhn and
Guillaume Latu Comparison of Numerical Solvers for
Anisotropic Diffusion Equations Arising
in Plasma Physics . . . . . . . . . . . 1091--1128
F. Guillén-González and
J. Koko A Splitting in Time Scheme and Augmented
Lagrangian Method for a Nematic Liquid
Crystal Problem . . . . . . . . . . . . 1129--1144
Zheng Chen and
Chi-Wang Shu Recovering Exponential Accuracy in
Fourier Spectral Methods Involving
Piecewise Smooth Functions with
Unbounded Derivative Singularities . . . 1145--1165
Morrakot Khebchareon and
Amiya K. Pani and
Graeme Fairweather Alternating Direction Implicit Galerkin
Methods for an Evolution Equation with a
Positive-Type Memory Term . . . . . . . 1166--1188
Yunhua Xue and
Cheng Wang and
Jian-Guo Liu Simple Finite Element Numerical
Simulation of Incompressible Flow Over
Non-rectangular Domains and the
Super-Convergence Analysis . . . . . . . 1189--1216
Graeme Fairweather and
Xuehua Yang and
Da Xu and
Haixiang Zhang An ADI Crank--Nicolson Orthogonal Spline
Collocation Method for the
Two-Dimensional Fractional
Diffusion-Wave Equation . . . . . . . . 1217--1239
Xiao-Yan Liu and
Andreas Karageorghis and
C. S. Chen A Kansa-Radial Basis Function Method for
Elliptic Boundary Value Problems in
Annular Domains . . . . . . . . . . . . 1240--1269
Gabriel N. Gatica and
Filánder A. Sequeira Analysis of an Augmented HDG Method for
a Class of Quasi-Newtonian Stokes Flows 1270--1308
Wenming He and
Zhimin Zhang and
Ren Zhao The Highest Superconvergence of the
Tri-linear Element for Schrödinger
Operator with Singularity . . . . . . . 1--18
Xudong Yao Ljusternik--Schnirelman Minimax
Algorithms and an Application for
Finding Multiple Negative Energy
Solutions of Semilinear Elliptic
Dirichlet Problem Involving Concave and
Convex Nonlinearities: Part I.
Algorithms and Convergence . . . . . . . 19--40
Hong-Kui Pang and
Hai-Wei Sun Fast Numerical Contour Integral Method
for Fractional Diffusion Equations . . . 41--66
Yanlai Chen and
Sigal Gottlieb and
Alfa Heryudono and
Akil Narayan A Reduced Radial Basis Function Method
for Partial Differential Equations on
Irregular Domains . . . . . . . . . . . 67--90
Elena Celledoni and
Bawfeh Kingsley Kometa and
Olivier Verdier High Order Semi-Lagrangian Methods for
the Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 91--115
Dmitry Kolomenskiy and
Jean-Christophe Nave and
Kai Schneider Adaptive Gradient-Augmented Level Set
Method with Multiresolution Error
Estimation . . . . . . . . . . . . . . . 116--140
Jiaxiang Cai and
Yushun Wang and
Yuezheng Gong Numerical Analysis of AVF Methods for
Three-Dimensional Time-Domain Maxwell's
Equations . . . . . . . . . . . . . . . 141--176
Pak-Wing Fok A Linearly Fourth Order Multirate
Runge--Kutta Method with Error Control 177--195
Dai-Qiang Chen and
Yan Zhou Wavelet Frame Based Image Restoration
via Combined Sparsity and Nonlocal Prior
of Coefficients . . . . . . . . . . . . 196--224
Victor Ginting and
Guang Lin and
Jiangguo Liu On Application of the Weak Galerkin
Finite Element Method to a Two-Phase
Model for Subsurface Flow . . . . . . . 225--239
W. Boscheri and
M. Dumbser An Efficient Quadrature-Free Formulation
for High Order
Arbitrary-Lagrangian--Eulerian
ADER--WENO Finite Volume Schemes on
Unstructured Meshes . . . . . . . . . . 240--274
Eric Blayo and
David Cherel and
Antoine Rousseau Towards Optimized Schwarz Methods for
the Navier--Stokes Equations . . . . . . 275--295
D. Olson and
S. Shukla and
G. Simpson and
D. Spirn Petviashvilli's Method for the Dirichlet
Problem . . . . . . . . . . . . . . . . 296--320
Bo Dong and
Chi-Wang Shu and
Wei Wang A New Multiscale Discontinuous Galerkin
Method for the One-Dimensional
Stationary Schrödinger Equation . . . . . 321--345
Weifeng Qiu and
Ke Shi An HDG Method for Convection Diffusion
Equation . . . . . . . . . . . . . . . . 346--357
Gianluca Geraci and
Pietro Marco Congedo and
Rémi Abgrall and
Gianluca Iaccarino A Novel Weakly-Intrusive Non-linear
Multiresolution Framework for
Uncertainty Quantification in Hyperbolic
Partial Differential Equations . . . . . 358--405
C. Michoski and
C. Dawson and
E. J. Kubatko and
D. Wirasaet and
S. Brus and
J. J. Westerink A Comparison of Artificial Viscosity,
Limiters, and Filters, for High Order
Discontinuous Galerkin Solutions in
Nonlinear Settings . . . . . . . . . . . 406--434
Tao Zhao A Spectral Analysis of Subspace Enhanced
Preconditioners . . . . . . . . . . . . 435--457
Mahboub Baccouch Recovery-Based Error Estimator for the
Discontinuous Galerkin Method for
Nonlinear Scalar Conservation Laws in
One Space Dimension . . . . . . . . . . 459--476
Xu-hong Yu and
Ben-yu Guo Spectral Method for Fourth-Order
Problems on Quadrilaterals . . . . . . . 477--503
Huadong Gao Unconditional Optimal Error Estimates of
BDF--Galerkin FEMs for Nonlinear
Thermistor Equations . . . . . . . . . . 504--527
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Local Error Estimates for the SUPG
Method Applied to Evolutionary
Convection--Reaction-Diffusion Equations 528--554
Zhen Dong Luo A Stabilized Crank--Nicolson Mixed
Finite Volume Element Formulation for
the Non-stationary Incompressible
Boussinesq Equations . . . . . . . . . . 555--576
Sara Mancini and
Francisco Bernal and
Juan A. Acebrón An Efficient Algorithm for Accelerating
Monte Carlo Approximations of the
Solution to Boundary Value Problems . . 577--597
Hongxia Liu and
Jianxian Qiu Finite Difference Hermite WENO Schemes
for Conservation Laws, II: an
Alternative Approach . . . . . . . . . . 598--624
Jeonghun J. Lee and
Hyea Hyun Kim Analysis of a Staggered Discontinuous
Galerkin Method for Linear Elasticity 625--649
Chang-Yeol Jung and
Thien Binh Nguyen New Time Differencing Methods for
Spectral Methods . . . . . . . . . . . . 650--671
Max D. Gunzburger and
Lisheng Hou and
Ju Ming Stochastic Steady-State Navier--Stokes
Equations with Additive Random Noise . . 672--691
M. Semplice and
A. Coco and
G. Russo Adaptive Mesh Refinement for Hyperbolic
Systems Based on Third-Order Compact
WENO Reconstruction . . . . . . . . . . 692--724
Seakweng Vong and
Pin Lyu and
Zhibo Wang A Compact Difference Scheme for
Fractional Sub-diffusion Equations with
the Spatially Variable Coefficient Under
Neumann Boundary Conditions . . . . . . 725--739
Jin Li and
Hongxing Rui and
Dehao Yu Trapezoidal Rule for Computing
Supersingular Integral on a Circle . . . 740--760
A. Baeza and
P. Mulet and
D. Zorío High Order Boundary Extrapolation
Technique for Finite Difference Methods
on Complex Domains with Cartesian Meshes 761--791
Florent Berthelin and
Thierry Goudon and
Sebastian Minjeaud Multifluid Flows: a Kinetic Approach . . 792--824
F. Lepe and
D. Mora and
R. Rodríguez Finite Element Analysis of a Bending
Moment Formulation for the Vibration
Problem of a Non-homogeneous Timoshenko
Beam . . . . . . . . . . . . . . . . . . 825--848
Zheng-Fen Jin and
Zhongping Wan and
Yuling Jiao and
Xiliang Lu An Alternating Direction Method with
Continuation for Nonconvex Low Rank
Minimization . . . . . . . . . . . . . . 849--869
Eric Chung and
Bernardo Cockburn and
Guosheng Fu The Staggered DG Method is the Limit of
a Hybridizable DG Method. Part II: The
Stokes Flow . . . . . . . . . . . . . . 870--887
Wei Deng and
Wotao Yin On the Global and Linear Convergence of
the Generalized Alternating Direction
Method of Multipliers . . . . . . . . . 889--916
L. E. Carr III and
C. F. Borges and
F. X. Giraldo Matrix-Free Polynomial-Based Nonlinear
Least Squares Optimized Preconditioning
and Its Application to Discontinuous
Galerkin Discretizations of the Euler
Equations . . . . . . . . . . . . . . . 917--940
Wei Gong and
Michael Hinze and
Zhaojie Zhou Finite Element Method and A Priori Error
Estimates for Dirichlet Boundary Control
Problems Governed by Parabolic PDEs . . 941--967
Hongfei Fu and
Hongxing Rui and
Jian Hou and
Haihong Li A Stabilized Mixed Finite Element Method
for Elliptic Optimal Control Problems 968--986
Hongfei Fu and
Hongxing Rui and
Jian Hou and
Haihong Li Erratum to: A Stabilized Mixed Finite
Element Method for Elliptic Optimal
Control Problems . . . . . . . . . . . . 987--990
Javier de Frutos and
Bosco García-Archilla and
Volker John and
Julia Novo Grad-div Stabilization for the
Evolutionary Oseen Problem with Inf-sup
Stable Finite Elements . . . . . . . . . 991--1024
Byungjoon Lee and
Myungjoo Kang Full 3D Simulations of Two-Phase
Core-Annular Flow in Horizontal Pipe
Using Level Set Method . . . . . . . . . 1025--1051
G. Puppo and
M. Semplice Well-Balanced High Order $1$D Schemes on
Non-uniform Grids and Entropy Residuals 1052--1076
Ben-yu Guo and
Yu-jian Jiao Spectral Method For Navier--Stokes
Equations With Non-slip Boundary
Conditions By Using Divergence-Free Base
Functions . . . . . . . . . . . . . . . 1077--1101
Daozhi Han A Decoupled Unconditionally Stable
Numerical Scheme for the
Cahn--Hilliard--Hele--Shaw System . . . 1102--1121
Xavier Warin Some Non-monotone Schemes for Time
Dependent Hamilton--Jacobi--Bellman
Equations in Stochastic Control . . . . 1122--1147
Cui-cui Ji and
Zhi-zhong Sun and
Zhao-peng Hao Numerical Algorithms with High Spatial
Accuracy for the Fourth-Order Fractional
Sub-Diffusion Equations with the First
Dirichlet Boundary Conditions . . . . . 1148--1174
Zaiwen Wen and
Chao Yang and
Xin Liu and
Yin Zhang Trace-Penalty Minimization for
Large-Scale Eigenspace Computation . . . 1175--1203
Bingsheng He and
Hong-Kun Xu and
Xiaoming Yuan On the Proximal Jacobian Decomposition
of ALM for Multiple-Block Separable
Convex Minimization Problems and Its
Relationship to ADMM . . . . . . . . . . 1204--1217
K. Baarman and
V. Havu and
T. Eirola Direct Minimization for Ensemble
Electronic Structure Calculations . . . 1218--1233
Ashish Bhatt and
Dwayne Floyd and
Brian E. Moore Second Order Conformal Symplectic
Schemes for Damped Hamiltonian Systems 1234--1259
P. F. Antonietti and
M. Grasselli and
S. Stangalino and
M. Verani Discontinuous Galerkin Approximation of
Linear Parabolic Problems with Dynamic
Boundary Conditions . . . . . . . . . . 1260--1280
Guang-hua Gao and
Zhi-zhong Sun Two Alternating Direction Implicit
Difference Schemes for Two-Dimensional
Distributed-Order Fractional Diffusion
Equations . . . . . . . . . . . . . . . 1281--1312
Ceren Gürkan and
Esther Sala-Lardies and
Martin Kronbichler and
Sonia Fernández-Méndez eXtended Hybridizable Discontinuous
Galerkin (X-HDG) for Void Problems . . . 1313--1333
Liyan Ma and
Tieyong Zeng Image Deblurring Via Total Variation
Based Structured Sparse Model Selection 1--19
Bishnu P. Lamichhane and
Stephen G. Roberts and
Linda Stals A Mixed Finite Element Discretisation of
Thin Plate Splines Based on Biorthogonal
Systems . . . . . . . . . . . . . . . . 20--42
Xianjuan Li and
Tao Tang and
Chuanju Xu Numerical Solutions for Weakly Singular
Volterra Integral Equations Using
Chebyshev and Legendre Pseudo-Spectral
Galerkin Methods . . . . . . . . . . . . 43--64
Yanping Chen and
Fenglin Huang Galerkin Spectral Approximation of
Elliptic Optimal Control Problems with $
H^1 $-Norm State Constraint . . . . . . 65--83
Oisin Tong and
Aaron Katz and
Yushi Yanagita and
Alex Casey and
Robert Schaap High-Order Methods for Turbulent Flows
on Three-Dimensional Strand Grids . . . 84--102
Haijuan Hu and
Bing Li and
Quansheng Liu Removing Mixture of Gaussian and Impulse
Noise by Patch-Based Weighted Means . . 103--129
Yu Du and
Lingxue Zhu Preasymptotic Error Analysis of High
Order Interior Penalty Discontinuous
Galerkin Methods for the Helmholtz
Equation with High Wave Number . . . . . 130--152
Chunjia Bi and
Cheng Wang and
Yanping Lin Pointwise Error Estimates and Two-Grid
Algorithms of Discontinuous Galerkin
Method for Strongly Nonlinear Elliptic
Problems . . . . . . . . . . . . . . . . 153--175
Andrey Kozelkov and
Vadim Kurulin and
Vladislav Emelyanov and
Elena Tyatyushkina and
Konstantin Volkov Comparison of Convective Flux
Discretization Schemes in Detached-Eddy
Simulation of Turbulent Flows on
Unstructured Meshes . . . . . . . . . . 176--191
Sergey Yakovlev and
David Moxey and
Robert M. Kirby and
Spencer J. Sherwin To CG or to HDG: a Comparative Study in
$3$D . . . . . . . . . . . . . . . . . . 192--220
H. Barkouki and
A. H. Bentbib and
K. Jbilou An Adaptive Rational Block Lanczos-Type
Algorithm for Model Reduction of Large
Scale Dynamical Systems . . . . . . . . 221--236
Mahsa Mirzargar and
Jennifer K. Ryan and
Robert M. Kirby Smoothness-Increasing
Accuracy-Conserving (SIAC) Filtering and
Quasi-Interpolation: a Unified View . . 237--261
Qian Zhang and
Zhilin Li and
Zhiyue Zhang A Sparse Grid Stochastic Collocation
Method for Elliptic Interface Problems
with Random Input . . . . . . . . . . . 262--280
Hongjin He and
Chen Ling and
Hong-Kun Xu An Implementable Splitting Algorithm for
the $ \ell_1$-norm Regularized Split
Feasibility Problem . . . . . . . . . . 281--298
Chang Ho Kim and
Youngsoo Ha and
Jungho Yoon Modified Non-linear Weights for
Fifth-Order Weighted Essentially
Non-oscillatory Schemes . . . . . . . . 299--323
Tzanio V. Kolev and
Jinchao Xu and
Yunrong Zhu Multilevel Preconditioners for
Reaction--Diffusion Problems with
Discontinuous Coefficients . . . . . . . 324--350
J. Romero and
K. Asthana and
A. Jameson A Simplified Formulation of the Flux
Reconstruction Method . . . . . . . . . 351--374
Raphaël Lamouroux and
Jérémie Gressier and
Gilles Grondin A High-Order Compact Limiter Based on
Spatially Weighted Projections for the
Spectral Volume and the Spectral
Differences Method . . . . . . . . . . . 375--403
Tongjun Sun and
Wanfang Shen and
Benxue Gong and
Wenbin Liu A Priori Error Estimate of Stochastic
Galerkin Method for Optimal Control
Problem Governed by Stochastic Elliptic
PDE with Constrained Control . . . . . . 405--431
Rick Archibald and
Anne Gelb and
Rodrigo B. Platte Image Reconstruction from Undersampled
Fourier Data Using the Polynomial
Annihilation Transform . . . . . . . . . 432--452
A. Alvarado and
P. Castillo Computational Performance of LDG Methods
Applied to Time Harmonic Maxwell
Equation in Polyhedral Domains . . . . . 453--474
Issei Oikawa Analysis of a Reduced-Order HDG Method
for the Stokes Equations . . . . . . . . 475--492
Gang Li and
Yulong Xing Well-Balanced Discontinuous Galerkin
Methods for the Euler Equations Under
Gravitational Fields . . . . . . . . . . 493--513
Andrew R. Winters and
Gregor J. Gassner An Entropy Stable Finite Volume Scheme
for the Equations of Shallow Water
Magnetohydrodynamics . . . . . . . . . . 514--539
Rong Wang and
Hui Feng and
Cong Huang A New Mapped Weighted Essentially
Non-oscillatory Method Using Rational
Mapping Function . . . . . . . . . . . . 540--580
Lei Wu and
Zhe Sun and
Dong-Hui Li A Barzilai--Borwein-Like Iterative Half
Thresholding Algorithm for the $ L_{1 /
2} $ Regularized Problem . . . . . . . . 581--601
Gangjoon Yoon and
Chohong Min Convergence Analysis of the Standard
Central Finite Difference Method for
Poisson Equation . . . . . . . . . . . . 602--617
Christophe Berthon and
Ana\"\is Crestetto and
Françoise Foucher A Well-Balanced Finite Volume Scheme for
a Mixed Hyperbolic/Parabolic System to
Model Chemotaxis . . . . . . . . . . . . 618--643
Shu-Lin Wu Convergence Analysis of the
Parareal-Euler Algorithm for Systems of
ODEs with Complex Eigenvalues . . . . . 644--668
Huoyuan Duan and
Fengjuan Qiu and
Roger C. E. Tan and
Weiying Zheng An Adaptive FEM for a Maxwell Interface
Problem . . . . . . . . . . . . . . . . 669--704
Hui Sun and
Shenggao Zhou and
David K. Moore and
Li-Tien Cheng and
Bo Li Numerical Treatment of Stokes Solvent
Flow and Solute--Solvent Interfacial
Dynamics for Nonpolar Molecules . . . . 705--723
Wansheng Wang and
Long Chen and
Jie Zhou Postprocessing Mixed Finite Element
Methods For Solving Cahn--Hilliard
Equation: Methods and Error Analysis . . 724--746
M. Eigel and
C. Merdon Equilibration a Posteriori Error
Estimation for
Convection--Diffusion-Reaction Problems 747--768
Abhishek Sheshadri and
Antony Jameson On the Stability of the Flux
Reconstruction Schemes on Quadrilateral
Elements for the Linear Advection
Equation . . . . . . . . . . . . . . . . 769--790
Abhishek Sheshadri and
Antony Jameson Erratum to: On the Stability of the Flux
Reconstruction Schemes on Quadrilateral
Elements for the Linear Advection
Equation . . . . . . . . . . . . . . . . 791--794
Pei Yang and
Tao Xiong and
Jing-Mei Qiu and
Zhengfu Xu High Order Maximum Principle Preserving
Finite Volume Method for Convection
Dominated Problems . . . . . . . . . . . 795--820
Xinguo Liu and
Jianping You Numerical Methods for the Genvar
Criterion of Multiple-Sets Canonical
Analysis . . . . . . . . . . . . . . . . 821--835
Tony Wong and
Shingyu Leung A Fast Sweeping Method for Eikonal
Equations on Implicit Surfaces . . . . . 837--859
Xiaomao Deng and
Xiao-Chuan Cai and
Jun Zou Two-Level Space--Time Domain
Decomposition Methods for
Three-Dimensional Unsteady Inverse
Source Problems . . . . . . . . . . . . 860--882
Jianliang Qian and
Lijun Yuan and
Yuan Liu and
Songting Luo and
Robert Burridge Babich's Expansion and High-Order
Eulerian Asymptotics for Point-Source
Helmholtz Equations . . . . . . . . . . 883--908
Seunggyu Lee and
Darae Jeong and
Wanho Lee and
Junseok Kim An Immersed Boundary Method for a
Contractile Elastic Ring in a
Three-Dimensional Newtonian Fluid . . . 909--925
Yin Tat Lee and
Ka Chun Lam and
Lok Ming Lui Landmark-Matching Transformation with
Large Deformation Via $n$-dimensional
Quasi-conformal Maps . . . . . . . . . . 926--954
Wolf-Jürgen Beyn and
Elena Isaak and
Raphael Kruse Stochastic $C$-Stability and
$B$-Consistency of Explicit and Implicit
Euler-Type Schemes . . . . . . . . . . . 955--987
Naveed Ahmed and
Gunar Matthies Numerical Study of SUPG and LPS Methods
Combined with Higher Order Variational
Time Discretization Schemes Applied to
Time-Dependent Linear
Convection--Diffusion-Reaction Equations 988--1018
Inmaculada Higueras and
Teo Roldán Construction of Additive Semi-Implicit
Runge--Kutta Methods with Low-Storage
Requirements . . . . . . . . . . . . . . 1019--1042
Liyong Zhu and
Lili Ju and
Weidong Zhao Fast High-Order Compact Exponential Time
Differencing Runge--Kutta Methods for
Second-Order Semilinear Parabolic
Equations . . . . . . . . . . . . . . . 1043--1065
Tao Xiong and
Jing-Mei Qiu and
Zhengfu Xu Parametrized Positivity Preserving Flux
Limiters for the High Order Finite
Difference WENO Scheme Solving
Compressible Euler Equations . . . . . . 1066--1088
Alfa Heryudono and
Elisabeth Larsson and
Alison Ramage and
Lina von Sydow Preconditioning for Radial Basis
Function Partition of Unity Methods . . 1089--1109
Jingjun Zhao and
Yang Cao and
Yang Xu Legendre Spectral Collocation Methods
for Volterra Delay--Integro-Differential
Equations . . . . . . . . . . . . . . . 1110--1133
Qinghai Zhang GePUP: Generic Projection and
Unconstrained PPE for Fourth-Order
Solutions of the Incompressible
Navier--Stokes Equations with No-Slip
Boundary Conditions . . . . . . . . . . 1134--1180
Jun Hu and
Yunqing Huang and
Rui Ma Guaranteed Lower Bounds for Eigenvalues
of Elliptic Operators . . . . . . . . . 1181--1197
Shi Jin and
Dongbin Xiu and
Xueyu Zhu A Well-Balanced Stochastic Galerkin
Method for Scalar Hyperbolic Balance
Laws with Random Inputs . . . . . . . . 1198--1218
I. Cravero and
M. Semplice On the Accuracy of WENO and CWENO
Reconstructions of Third Order on
Nonuniform Meshes . . . . . . . . . . . 1219--1246
Tian-jun Wang A Spectral Method for Fourth-Order Mixed
Inhomogeneous Boundary Value Problem in
Three Dimensions . . . . . . . . . . . . 1247--1271
G. Mengaldo and
D. De Grazia and
P. E. Vincent and
S. J. Sherwin On the Connections Between Discontinuous
Galerkin and Flux Reconstruction
Schemes: Extension to Curvilinear Meshes 1272--1292
Ning Du and
Hong Wang and
Wenbin Liu A Fast Gradient Projection Method for a
Constrained Fractional Optimal Control 1--20
Alexandre Janon and
Maëlle Nodet and
Clémentine Prieur Goal-Oriented Error Estimation for the
Reduced Basis Method, with Application
to Sensitivity Analysis . . . . . . . . 21--41
Ulrik S. Fjordholm and
Deep Ray A Sign Preserving WENO Reconstruction
Method . . . . . . . . . . . . . . . . . 42--63
Alessandro Lanza and
Serena Morigi and
Fiorella Sgallari Constrained TV$_p$--$ \ell_2$ Model for
Image Restoration . . . . . . . . . . . 64--91
François Bouchut and
Xavier Lhébrard A $5$-Wave Relaxation Solver for the
Shallow Water MHD System . . . . . . . . 92--115
Pengtao Sun and
Yuzhou Sun Asymptotic Analysis and Error Estimates
of Mixed Finite Element Method for
Brinkman Model . . . . . . . . . . . . . 116--142
Paola F. Antonietti and
Blanca Ayuso de Dios and
Ilario Mazzieri and
Alfio Quarteroni Stability Analysis of Discontinuous
Galerkin Approximations to the
Elastodynamics Problem . . . . . . . . . 143--170
David C. Seal and
Qi Tang and
Zhengfu Xu and
Andrew J. Christlieb An Explicit High-Order Single-Stage
Single-Step Positivity-Preserving Finite
Difference WENO Method for the
Compressible Euler Equations . . . . . . 171--190
Ali Samii and
Nishant Panda and
Craig Michoski and
Clint Dawson A Hybridized Discontinuous Galerkin
Method for the Nonlinear Korteweg--de
Vries Equation . . . . . . . . . . . . . 191--212
Payel Das and
Mitali Madhumita Sahani and
Gnaneshwar Nelakanti and
Guangqing Long Legendre Spectral Projection Methods for
Fredholm--Hammerstein Integral Equations 213--230
Adam M. Oberman and
Ian Zwiers Adaptive Finite Difference Methods for
Nonlinear Elliptic and Parabolic Partial
Differential Equations with Free
Boundaries . . . . . . . . . . . . . . . 231--251
Bo Yu and
Xiaoyun Jiang Numerical Identification of the
Fractional Derivatives in the
Two-Dimensional Fractional Cable
Equation . . . . . . . . . . . . . . . . 252--272
Chang-Ock Lee and
Jong Ho Lee and
Hyenkyun Woo and
Sangwoon Yun Block Decomposition Methods for Total
Variation by Primal-Dual Stitching . . . 273--302
Norbert Heuer and
Salim Meddahi and
Francisco-Javier Sayas Symmetric Coupling of LDG--FEM and
DG--BEM . . . . . . . . . . . . . . . . 303--325
Hongrui Geng and
Xia Ji and
Jiguang Sun and
Liwei Xu $ C^0 $ IP Methods for the Transmission
Eigenvalue Problem . . . . . . . . . . . 326--338
Guanyu Zhou and
Takahito Kashiwabara and
Issei Oikawa Penalty Method for the Stationary
Navier--Stokes Problems Under the Slip
Boundary Condition . . . . . . . . . . . 339--374
Hongtao Chen and
Zhimin Zhang and
Qingsong Zou A Recovery Based Linear Finite Element
Method For $1$D Bi-Harmonic Problems . . 375--394
Roberto Cavoretto and
Alessandra De Rossi and
Emma Perracchione and
Ezio Venturino Robust Approximation Algorithms for the
Detection of Attraction Basins in
Dynamical Systems . . . . . . . . . . . 395--415
Lina Hu and
Lina Ma and
Jie Shen Efficient Spectral-Galerkin Method and
Analysis for Elliptic PDEs with
Non-local Boundary Conditions . . . . . 417--437
Wei Yang and
Yunqing Huang and
Jichun Li Developing a Time-Domain Finite Element
Method for the Lorentz Metamaterial
Model and Applications . . . . . . . . . 438--463
Xiaofeng Cai and
Xiangxiong Zhang and
Jianxian Qiu Positivity-Preserving High Order Finite
Volume HWENO Schemes for Compressible
Euler Equations . . . . . . . . . . . . 464--483
Wenzhen Qu and
Namdi Brandon and
Dangxing Chen and
Jingfang Huang and
Tyler Kress A Numerical Framework for Integrating
Deferred Correction Methods to Solve
High Order Collocation Formulations of
ODEs . . . . . . . . . . . . . . . . . . 484--520
Zhiqiang Sheng and
Guangwei Yuan A Cell-Centered Nonlinear Finite Volume
Scheme Preserving Fully Positivity for
Diffusion Equation . . . . . . . . . . . 521--545
Shiqian Ma Alternating Proximal Gradient Method for
Convex Minimization . . . . . . . . . . 546--572
Shunsuke Hayashi and
Soon-Yi Wu and
Liping Zhang Computation Algorithm for Convex
Semi-infinite Program with Second-Order
Cones: Special Analyses for Affine and
Quadratic Case . . . . . . . . . . . . . 573--595
J. Winokur and
D. Kim and
F. Bisetti and
O. P. Le Ma\^\itre and
O. M. Knio Sparse Pseudo Spectral Projection
Methods with Directional Adaptation for
Uncertainty Quantification . . . . . . . 596--623
B. Schmidtmann and
B. Seibold and
M. Torrilhon Relations Between WENO3 and Third-Order
Limiting in Finite Volume Methods . . . 624--652
Swapan K. Pandit and
Hemanta Karmakar An Efficient Implicit Compact
Streamfunction Velocity Formulation of
Two Dimensional Flows . . . . . . . . . 653--688
Weiyang Ding and
Yimin Wei Solving Multi-linear Systems with $
\mathcal {M}$-Tensors . . . . . . . . . 689--715
Yannan Chen and
Liqun Qi and
Qun Wang Computing Extreme Eigenvalues of Large
Scale Hankel Tensors . . . . . . . . . . 716--738
Bart S. van Lith and
Jan H. M. ten Thije Boonkkamp and
Wilbert L. IJzerman and
Teus W. Tukker A Novel Scheme for Liouville's Equation
with a Discontinuous Hamiltonian and
Applications to Geometrical Optics . . . 739--771
Ying He and
Misun Min and
David P. Nicholls A Spectral Element Method with
Transparent Boundary Condition for
Periodic Layered Media Scattering . . . 772--802
Jie Chen and
Lois C. McInnes and
Hong Zhang Analysis and Practical Use of Flexible
BiCGStab . . . . . . . . . . . . . . . . 803--825
Shuqin Wang and
Jinyun Yuan and
Weihua Deng and
Yujiang Wu A Hybridized Discontinuous Galerkin
Method for $2$D Fractional
Convection-Diffusion Equations . . . . . 826--847
S. C. Brenner and
J. Gedicke and
L.-Y. Sung An Adaptive \boldmath $ P_1 $ Finite
Element Method for Two-Dimensional
Transverse Magnetic Time Harmonic
Maxwell's Equations with General
Material Properties and General Boundary
Conditions . . . . . . . . . . . . . . . 848--863
Miyoun Jung and
Myungjoo Kang Variational Image Colorization Models
Using Higher-Order Mumford--Shah
Regularizers . . . . . . . . . . . . . . 864--888
Alex Shum and
Kirsten Morris and
Amir Khajepour Convergence Rate for the Ordered Upwind
Method . . . . . . . . . . . . . . . . . 889--913
Andrew J. Christlieb and
Sigal Gottlieb and
Zachary Grant and
David C. Seal Explicit Strong Stability Preserving
Multistage Two-Derivative Time-Stepping
Schemes . . . . . . . . . . . . . . . . 914--942
Andrew J. Christlieb and
Sigal Gottlieb and
Zachary Grant and
David C. Seal Erratum to: Explicit Strong Stability
Preserving Multistage Two-Derivative
Time-Stepping Schemes . . . . . . . . . 943--944
Mahboub Baccouch A Posteriori Error Analysis of the
Discontinuous Galerkin Method for
Two-Dimensional Linear Hyperbolic
Conservation Laws on Cartesian Grids . . 945--974
Sebastiano Boscarino and
Francis Filbet and
Giovanni Russo High Order Semi-implicit Schemes for
Time Dependent Partial Differential
Equations . . . . . . . . . . . . . . . 975--1001
Siyang Wang and
Kristoffer Virta and
Gunilla Kreiss High Order Finite Difference Methods for
the Wave Equation with Non-conforming
Grid Interfaces . . . . . . . . . . . . 1002--1028
Ruihan Guo and
Francis Filbet and
Yan Xu Efficient High Order Semi-implicit Time
Discretization and Local Discontinuous
Galerkin Methods for Highly Nonlinear
PDEs . . . . . . . . . . . . . . . . . . 1029--1054
Wei Xu and
Ning Zheng and
Ken Hayami Jacobian-Free Implicit Inner-Iteration
Preconditioner for Nonlinear Least
Squares Problems . . . . . . . . . . . . 1055--1081
Yifei Lou and
Penghang Yin and
Jack Xin Point Source Super-resolution Via
Non-convex $ L_1 $ Based Methods . . . . 1082--1100
Maya Briani and
Benedetto Piccoli and
Jing-Mei Qiu Notes on RKDG Methods for Shallow-Water
Equations in Canal Networks . . . . . . 1101--1123
Ali W. K. Sangawi and
Ali H. M. Murid and
Lee Khiy Wei Fast Computing of Conformal Mapping and
Its Inverse of Bounded Multiply
Connected Regions onto Second, Third and
Fourth Categories of Koebe's Canonical
Slit Regions . . . . . . . . . . . . . . 1124--1141
Ali W. K. Sangawi and
Ali H. M. Murid and
Lee Khiy Wei Erratum to: Fast Computing of Conformal
Mapping and Its Inverse of Bounded
Multiply Connected Regions onto Second,
Third and Fourth Categories of Koebe's
Canonical Slit Regions . . . . . . . . . 1142--1143
Chunmei Wang and
Junping Wang Discretization of div-curl Systems by
Weak Galerkin Finite Element Methods on
Polyhedral Partitions . . . . . . . . . 1144--1171
Li Chen and
Ruo Li An Integrated Linear Reconstruction for
Finite Volume Scheme on Unstructured
Grids . . . . . . . . . . . . . . . . . 1172--1197
Li Chen and
Ruo Li Erratum to: An Integrated Linear
Reconstruction for Finite Volume Scheme
on Unstructured Grids . . . . . . . . . 1198--1199
Zhi Li and
Yifei Lou and
Tieyong Zeng Variational Multiplicative Noise Removal
by DC Programming . . . . . . . . . . . 1200--1216
Hailiang Liu and
Zhongming Wang An Entropy Satisfying Discontinuous
Galerkin Method for Nonlinear
Fokker--Planck Equations . . . . . . . . 1217--1240
Jia Zhao and
Qi Wang Semi-Discrete Energy-Stable Schemes for
a Tensor-Based Hydrodynamic Model of
Nematic Liquid Crystal Flows . . . . . . 1241--1266
S. Barbier and
A. Rapaport and
A. Rousseau Modelling of Biological Decontamination
of a Water Resource in Natural
Environment and Related Feedback
Strategies . . . . . . . . . . . . . . . 1267--1280
Hermann Brunner and
Tao Tang and
Jiwei Zhang Numerical Blow-Up of Nonlinear Parabolic
Integro-Differential Equations on
Unbounded Domain . . . . . . . . . . . . 1281--1298
Jin Zhang and
Xiaowei Liu Analysis of SDFEM on Shishkin Triangular
Meshes and Hybrid Meshes for Problems
with Characteristic Layers . . . . . . . 1299--1316
Rong An Optimal Error Estimates of Linearized
Crank--Nicolson Galerkin Method for
Landau--Lifshitz Equation . . . . . . . 1--27
Yanping Chen and
Jiaoyan Zeng and
Jie Zhou $ L^p $ Error Estimates of Two-Grid
Method for Miscible Displacement Problem 28--51
Tianyi Lin and
Shiqian Ma and
Shuzhong Zhang Iteration Complexity Analysis of
Multi-block ADMM for a Family of Convex
Minimization Without Strong Convexity 52--81
Fang Li and
Stanley Osher and
Jing Qin and
Ming Yan A Multiphase Image Segmentation Based on
Fuzzy Membership Functions and $ L_1
$-Norm Fidelity . . . . . . . . . . . . 82--106
Yijing Zhou and
Wei Cai Numerical Solution of the Robin Problem
of Laplace Equations with a Feynman--Kac
Formula and Reflecting Brownian Motions 107--121
Mapundi K. Banda and
Axel-Stefan Häck and
Michael Herty Numerical Discretization of Coupling
Conditions by High-Order Schemes . . . . 122--145
Jonathan Thorne and
Aaron Katz Source Term Discretization Effects on
the Steady-State Accuracy of Finite
Volume Schemes . . . . . . . . . . . . . 146--169
A. Baeza and
P. Mulet and
D. Zorío High Order Weighted Extrapolation for
Boundary Conditions for Finite
Difference Methods on Complex Domains
with Cartesian Meshes . . . . . . . . . 170--200
Bin Zheng and
Luoping Chen and
Xiaozhe Hu and
Long Chen and
Ricardo H. Nochetto and
Jinchao Xu Fast Multilevel Solvers for a Class of
Discrete Fourth Order Parabolic Problems 201--226
Dajana Conte and
Beatrice Paternoster Modified Gauss--Laguerre Exponential
Fitting Based Formulae . . . . . . . . . 227--243
Helene Dallmann and
Daniel Arndt Stabilized Finite Element Methods for
the Oberbeck--Boussinesq Model . . . . . 244--273
Seongju Do and
Youngsoo Ha and
M. Kang and
Chang Ho Kim Application of a Multi-dimensional
Limiting Process to Central-Upwind
Schemes for Solving Hyperbolic Systems
of Conservation Laws . . . . . . . . . . 274--291
Jan S. Hesthaven and
Shun Zhang On the Use of ANOVA Expansions in
Reduced Basis Methods for Parametric
Partial Differential Equations . . . . . 292--313
Emmanuel Franck and
Laura S. Mendoza Finite Volume Scheme with Local High
Order Discretization of the Hydrostatic
Equilibrium for the Euler Equations with
External Forces . . . . . . . . . . . . 314--354
Zhenhua Chai and
Baochang Shi and
Zhaoli Guo A Multiple-Relaxation-Time Lattice
Boltzmann Model for General Nonlinear
Anisotropic Convection--Diffusion
Equations . . . . . . . . . . . . . . . 355--390
Myoungho Yoon and
Gangjoon Yoon and
Chohong Min On Solving the Singular System Arisen
from Poisson Equation with Neumann
Boundary Condition . . . . . . . . . . . 391--405
Jhuma Sen Gupta and
Rajen K. Sinha and
G. M. M. Reddy and
Jinank Jain A Posteriori Error Analysis of Two-Step
Backward Differentiation Formula Finite
Element Approximation for Parabolic
Interface Problems . . . . . . . . . . . 406--429
Nella Rotundo and
Tae-Yeon Kim and
Wen Jiang and
Luca Heltai and
Eliot Fried Error Analysis of a B-Spline Based
Finite-Element Method for Modeling
Wind-Driven Ocean Circulation . . . . . 430--459
Dai-Qiang Chen Data-Driven Tight Frame Learning Scheme
Based on Local and Non-local Sparsity
with Application to Image Recovery . . . 461--486
Jordan M. Martel and
Rodrigo B. Platte Stability of Radial Basis Function
Methods for Convection Problems on the
Circle and Sphere . . . . . . . . . . . 487--505
Guang-hua Gao and
Zhi-zhong Sun Two Alternating Direction Implicit
Difference Schemes for Solving the
Two-Dimensional Time Distributed-Order
Wave Equations . . . . . . . . . . . . . 506--531
Yuping Duan and
Huibin Chang and
Xue-Cheng Tai Convergent Non-overlapping Domain
Decomposition Methods for Variational
Image Segmentation . . . . . . . . . . . 532--555
Hayden Schaeffer and
Thomas Y. Hou An Accelerated Method for Nonlinear
Elliptic PDE . . . . . . . . . . . . . . 556--580
Mani Razi and
Peter Attar and
Prakash Vedula Numerical Solution of Multidimensional
Hyperbolic PDEs Using Defect Correction
on Adaptive Grids . . . . . . . . . . . 581--609
Jeonghun J. Lee Robust Error Analysis of Coupled Mixed
Methods for Biot's Consolidation Model 610--632
Nathan Albin and
Joshua Klarmann An Algorithmic Exploration of the
Existence of High-Order Summation by
Parts Operators with Diagonal Norm . . . 633--650
Yu Fu and
Weidong Zhao and
Tao Zhou Multistep Schemes for Forward Backward
Stochastic Differential Equations with
Jumps . . . . . . . . . . . . . . . . . 651--672
Sonia Seyed Allaei and
Teresa Diogo and
Magda Rebelo The Jacobi Collocation Method for a
Class of Nonlinear Volterra Integral
Equations with Weakly Singular Kernel 673--695
Wanshan Li and
Dong Liang Symmetric Energy--Conserved S-FDTD
Scheme for Two-Dimensional Maxwell's
Equations in Negative Index
Metamaterials . . . . . . . . . . . . . 696--735
Dong Lu and
Yong-Tao Zhang Krylov Integration Factor Method on
Sparse Grids for High Spatial Dimension
Convection--Diffusion Equations . . . . 736--763
Marc O. Delchini and
Jean C. Ragusa and
Ray A. Berry Viscous Regularization for the
Non-equilibrium Seven-Equation Two-Phase
Flow Model . . . . . . . . . . . . . . . 764--804
Claus R. Goetz and
Michael Dumbser A Novel Solver for the Generalized
Riemann Problem Based on a Simplified
LeFloch--Raviart Expansion and a Local
Space--Time Discontinuous Galerkin
Formulation . . . . . . . . . . . . . . 805--840
Xiaobing Feng and
Cody Lorton An Unconditionally Stable Discontinuous
Galerkin Method for the Elastic
Helmholtz Equations with Large Frequency 841--865
Alexander Jaust and
Jochen Schütz and
David C. Seal Implicit Multistage Two-Derivative
Discontinuous Galerkin Schemes for
Viscous Conservation Laws . . . . . . . 866--891
Gerard Awanou On Standard Finite Difference
Discretizations of the Elliptic
Monge--Amp\`ere Equation . . . . . . . . 892--904
F. D. Witherden and
J. S. Park and
P. E. Vincent An Analysis of Solution Point
Coordinates for Flux Reconstruction
Schemes on Tetrahedral Elements . . . . 905--920
Yuezheng Gong and
Xinfeng Liu and
Qi Wang Fully Discretized Energy Stable Schemes
for Hydrodynamic Equations Governing
Two-Phase Viscous Fluid Flows . . . . . 921--945
Matthieu Brachet and
Jean-Paul Chehab Stabilized Times Schemes for High
Accurate Finite Differences Solutions of
Nonlinear Parabolic Equations . . . . . 946--982
Weitao Chen and
Ching-Shan Chou and
Chiu-Yen Kao Minimizing Eigenvalues for Inhomogeneous
Rods and Plates . . . . . . . . . . . . 983--1013
Likun Hou and
Hao Gao and
Xiaoqun Zhang A Two-Stage Low Rank Approach for
Calibrationless Dynamic Parallel
Magnetic Resonance Image Reconstruction 1014--1032
Stefano Zaghi and
Andrea Di Mascio and
Bernardo Favini Application of
WENO--Positivity-Preserving Schemes to
Highly Under-Expanded Jets . . . . . . . 1033--1057
J. K. Djoko and
J. M. Lubuma and
M. Mbehou On the Numerical Solution of the
Stationary Power-Law Stokes Equations: a
Penalty Finite Element Approach . . . . 1058--1082
Kelong Cheng and
Cheng Wang and
Steven M. Wise and
Xingye Yue A Second-Order, Weakly Energy-Stable
Pseudo-spectral Scheme for the
Cahn--Hilliard Equation and Its Solution
by the Homogeneous Linear Iteration
Method . . . . . . . . . . . . . . . . . 1083--1114
John P. Boyd Tracing Multiple Solution Branches for
Nonlinear Ordinary Differential
Equations: Chebyshev and Fourier
Spectral Methods and a Degree-Increasing
Spectral Homotopy [DISH] . . . . . . . . 1115--1143
Hong-lin Liao and
Ying Zhao and
Xing-hu Teng A Weighted ADI Scheme for Subdiffusion
Equations . . . . . . . . . . . . . . . 1144--1164
Alexandra Tcheng and
Jean-Christophe Nave A Low Complexity Algorithm for
Non-Monotonically Evolving Fronts . . . 1165--1191
Gabriel N. Gatica and
Filánder A. Sequeira A Priori and a Posteriori Error Analyses
of an Augmented HDG Method for a Class
of Quasi-Newtonian Stokes Flows . . . . 1192--1250
Xuehai Huang and
Jianguo Huang A Superconvergent $ C^0 $ Discontinuous
Galerkin Method for Kirchhoff Plates:
Error Estimates, Hybridization and
Postprocessing . . . . . . . . . . . . . 1251--1278
Jiayu Han and
Yidu Yang An Adaptive Finite Element Method for
the Transmission Eigenvalue Problem . . 1279--1300
Tao Sun and
Roberto Barrio and
Hao Jiang and
Lizhi Cheng Local Linear Convergence of a
Primal--Dual Algorithm for the Augmented
Convex Models . . . . . . . . . . . . . 1301--1315
Yujie Zhang and
Wenjing Ye A High-Order Level-Set Method with
Enhanced Stability for Curvature Driven
Flows and Surface Diffusion Motion . . . 1316--1345
Hongqiang Zhu and
Jianxian Qiu and
Jing-Mei Qiu An $h$-Adaptive RKDG Method for the
Vlasov--Poisson System . . . . . . . . . 1346--1365
Jun Hu and
Xueqin Yang and
Shuo Zhang Capacity of the Adini Element for
Biharmonic Equations . . . . . . . . . . 1366--1383
Weifeng Qiu and
Manuel Solano and
Patrick Vega A High Order HDG Method for
Curved-Interface Problems Via
Approximations from Straight
Triangulations . . . . . . . . . . . . . 1384--1407
Jochen Garcke and
Axel Kröner Suboptimal Feedback Control of PDEs by
Solving HJB Equations on Adaptive Sparse
Grids . . . . . . . . . . . . . . . . . 1--28
Houssem Haddar and
Zixian Jiang and
Mohamed Kamel Riahi A Robust Inversion Method for
Quantitative $3$D Shape Reconstruction
from Coaxial Eddy Current Measurements 29--59
Hengguang Li and
Qinghui Zhang Optimal Quadrilateral Finite Elements on
Polygonal Domains . . . . . . . . . . . 60--84
Dongyang Shi and
Junjun Wang and
Fengna Yan Unconditional Superconvergence Analysis
for Nonlinear Parabolic Equation with $
{\rm EQ}_1^{rot} $ Nonconforming Finite
Element . . . . . . . . . . . . . . . . 85--111
Qingsong Zou An Unconditionally Stable Quadratic
Finite Volume Scheme over Triangular
Meshes for Elliptic Equations . . . . . 112--124
Hailong Guo and
Zhimin Zhang and
Ren Zhao Superconvergent Two-Grid Methods for
Elliptic Eigenvalue Problems . . . . . . 125--148
Qili Tang and
Yunqing Huang Local and Parallel Finite Element
Algorithm Based on Oseen-Type Iteration
for the Stationary Incompressible MHD
Flow . . . . . . . . . . . . . . . . . . 149--174
Jiangxing Wang and
Chuanmiao Chen and
Ziqing Xie The Highest Superconvergence Analysis of
ADG Method for Two Point Boundary Values
Problem . . . . . . . . . . . . . . . . 175--191
Yujie Wang and
Fuming Ma and
Enxi Zheng Galerkin Method for the Scattering
Problem of a Slit . . . . . . . . . . . 192--209
S. R. Brus and
D. Wirasaet and
J. J. Westerink and
C. Dawson Performance and Scalability Improvements
for Discontinuous Galerkin Solutions to
Conservation Laws on Unstructured Grids 210--242
J. Chang and
S. Karra and
K. B. Nakshatrala Large-Scale Optimization-Based
Non-negative Computational Framework for
Diffusion Equations: Parallel
Implementation and Performance Studies 243--271
Min Tang and
Yihong Wang Uniform Convergent Tailored Finite Point
Method for Advection--Diffusion Equation
with Discontinuous, Anisotropic and
Vanishing Diffusivity . . . . . . . . . 272--300
Dong Li and
Zhonghua Qiao On Second Order Semi-implicit Fourier
Spectral Methods for $2$D Cahn--Hilliard
Equations . . . . . . . . . . . . . . . 301--341
Jingtang Ma A New Finite Element Analysis for
Inhomogeneous Boundary-Value Problems of
Space Fractional Differential Equations 342--354
Daniel Baffet and
Jan S. Hesthaven High-Order Accurate Local Schemes for
Fractional Differential Equations . . . 355--385
Zhengang Zhao and
Yunying Zheng and
Peng Guo A Galerkin Finite Element Method for a
Class of Time--Space Fractional
Differential Equation with Nonsmooth
Data . . . . . . . . . . . . . . . . . . 386--406
Yanmin Zhao and
Pan Chen and
Weiping Bu and
Xiangtao Liu and
Yifa Tang Two Mixed Finite Element Methods for
Time-Fractional Diffusion Equations . . 407--428
Hong Wang and
Danping Yang and
Shengfeng Zhu Accuracy of Finite Element Methods for
Boundary-Value Problems of Steady-State
Fractional Diffusion Equations . . . . . 429--449
Jing Zhang and
Li-Lian Wang and
Huiyuan Li and
Zhimin Zhang Optimal Spectral Schemes Based on
Generalized Prolate Spheroidal Wave
Functions of Order $ - 1 $ . . . . . . . 451--477
Junyu Zhang and
Zaiwen Wen and
Yin Zhang Subspace Methods with Local Refinements
for Eigenvalue Computation Using
Low-Rank Tensor-Train Format . . . . . . 478--499
Xiaocui Li and
Xiaoyuan Yang and
Yinghan Zhang Error Estimates of Mixed Finite Element
Methods for Time-Fractional
Navier--Stokes Equations . . . . . . . . 500--515
C. Michoski and
A. Alexanderian and
C. Paillet and
E. J. Kubatko and
C. Dawson Stability of Nonlinear
Convection--Diffusion--Reaction Systems
in Discontinuous Galerkin Methods . . . 516--550
Jingyang Guo and
Jae-Hun Jung Radial Basis Function ENO and WENO
Finite Difference Methods Based on the
Optimization of Shape Parameters . . . . 551--575
Tingting Li and
Chi-Wang Shu and
Mengping Zhang Stability Analysis of the Inverse
Lax--Wendroff Boundary Treatment for
High Order Central Difference Schemes
for Diffusion Equations . . . . . . . . 576--607
Paola F. Antonietti and
Marco Sarti and
Marco Verani and
Ludmil T. Zikatanov A Uniform Additive Schwarz
Preconditioner for High-Order
Discontinuous Galerkin Approximations of
Elliptic Problems . . . . . . . . . . . 608--630
Zheng Liu and
Huayan Zhang and
Chunlin Wu On Geodesic Curvature Flow with Level
Set Formulation Over Triangulated
Surfaces . . . . . . . . . . . . . . . . 631--661
Lunji Song and
Chaoxia Yang Convergence of a Second-Order Linearized
BDF--IPDG for Nonlinear Parabolic
Equations with Discontinuous
Coefficients . . . . . . . . . . . . . . 662--685
Cheng Wang and
Pengtao Sun A Fictitious Domain Method with
Distributed Lagrange Multiplier for
Parabolic Problems With Moving
Interfaces . . . . . . . . . . . . . . . 686--716
Haijian Yang and
Xiao-Chuan Cai Two-Level Space--Time Domain
Decomposition Methods for Flow Control
Problems . . . . . . . . . . . . . . . . 717--743
Hongying Huang and
Zheng Chen and
Jin Li and
Jue Yan Direct Discontinuous Galerkin Method and
Its Variations for Second Order Elliptic
Equations . . . . . . . . . . . . . . . 744--765
Eric T. Chung and
Jie Du and
Man Chun Yuen An Adaptive SDG Method for the Stokes
System . . . . . . . . . . . . . . . . . 766--792
Chao Zhang and
Wenjie Liu and
Li-Lian Wang A New Collocation Scheme Using
Non-polynomial Basis Functions . . . . . 793--818
Enrique Fernández-Cara and
Arnaud Münch and
Diego A. Souza On the Numerical Controllability of the
Two-Dimensional Heat, Stokes and
Navier--Stokes Equations . . . . . . . . 819--858
L. Bonaventura and
A. Della Rocca Unconditionally Strong Stability
Preserving Extensions of the TR--BDF2
Method . . . . . . . . . . . . . . . . . 859--895
Matthew Causley and
Andrew Christlieb and
Eric Wolf Method of Lines Transpose: an Efficient
Unconditionally Stable Solver for Wave
Propagation . . . . . . . . . . . . . . 896--921
Zhongjie Lu and
A. Cesmelioglu and
J. J. W. Van der Vegt and
Yan Xu Discontinuous Galerkin Approximations
for Computing Electromagnetic Bloch
Modes in Photonic Crystals . . . . . . . 922--964
Daozhi Han and
Alex Brylev and
Xiaofeng Yang and
Zhijun Tan Numerical Analysis of Second Order,
Fully Discrete Energy Stable Schemes for
Phase Field Models of Two-Phase
Incompressible Flows . . . . . . . . . . 965--989
Ian N. Zwaan and
Michiel E. Hochstenbach Multidirectional Subspace Expansion for
One-Parameter and Multiparameter
Tikhonov Regularization . . . . . . . . 990--1009
Huangxin Chen and
Weifeng Qiu and
Ke Shi and
Manuel Solano A Superconvergent HDG Method for the
Maxwell Equations . . . . . . . . . . . 1010--1029
Lizhen Chen and
Jing An and
Qingqu Zhuang Direct Solvers for the Biharmonic
Eigenvalue Problems Using Legendre
Polynomials . . . . . . . . . . . . . . 1030--1041
Wolf-Jürgen Beyn and
Elena Isaak and
Raphael Kruse Stochastic $C$-Stability and
$B$-Consistency of Explicit and Implicit
Milstein-Type Schemes . . . . . . . . . 1042--1077
Benjamin Ivorra and
Susana Gomez and
Roland Glowinski and
Angel Manuel Ramos Nonlinear Advection--Diffusion--Reaction
Phenomena Involved in the Evolution and
Pumping of Oil in Open Sea: Modeling,
Numerical Simulation and Validation
Considering the Prestige and Oleg
Naydenov Oil Spill Cases . . . . . . . . 1078--1104
Michal Bra\'s and
Giuseppe Izzo and
Zdzislaw Jackiewicz Accurate Implicit--Explicit General
Linear Methods with Inherent
Runge--Kutta Stability . . . . . . . . . 1105--1143
Haiyan Su and
Xinlong Feng and
Jianping Zhao Two-Level Penalty Newton Iterative
Method for the $2$D/$3$D Stationary
Incompressible Magnetohydrodynamics
Equations . . . . . . . . . . . . . . . 1144--1179
Kejia Pan and
Dongdong He and
Hongling Hu An Extrapolation Cascadic Multigrid
Method Combined with a Fourth-Order
Compact Scheme for $3$D Poisson Equation 1180--1203
Qia Li and
Yuesheng Xu and
Na Zhang Two-Step Fixed-Point Proximity
Algorithms for Multi-block Separable
Convex Problems . . . . . . . . . . . . 1204--1228
Miyoun Jung Piecewise-Smooth Image Segmentation
Models with $ L^1 $ Data-Fidelity Terms 1229--1261
Matthias Sonntag and
Claus-Dieter Munz Efficient Parallelization of a Shock
Capturing for Discontinuous Galerkin
Methods using Finite Volume Sub-cells 1262--1289
Tonatiuh Sánchez-Vizuet and
Francisco-Javier Sayas Symmetric Boundary-Finite Element
Discretization of Time Dependent
Acoustic Scattering by Elastic Obstacles
with Piezoelectric Behavior . . . . . . 1290--1315
Xuping Zhang and
Jintao Zhang and
Bo Yu Symmetric Homotopy Method for
Discretized Elliptic Equations with
Cubic and Quintic Nonlinearities . . . . 1316--1335
Liyan Ma and
Li Xu and
Tieyong Zeng Low Rank Prior and Total Variation
Regularization for Image Deblurring . . 1336--1357
Jean-Luc Guermond and
Bojan Popov and
Yong Yang The Effect of the Consistent Mass Matrix
on the Maximum-Principle for Scalar
Conservation Equations . . . . . . . . . 1358--1366
Jia Zhao and
Huiyuan Li and
Qi Wang and
Xiaofeng Yang Decoupled Energy Stable Schemes for a
Phase Field Model of Three-Phase
Incompressible Viscous Fluid Flow . . . 1367--1389
Klaus Kaiser and
Jochen Schütz and
Ruth Schöbel and
Sebastian Noelle A New Stable Splitting for the
Isentropic Euler Equations . . . . . . . 1390--1407
Junjie Ma and
Shuhuang Xiang A Collocation Boundary Value Method for
Linear Volterra Integral Equations . . . 1--20
Timo Heister and
Muhammad Mohebujjaman and
Leo G. Rebholz Decoupled, Unconditionally Stable,
Higher Order Discretizations for MHD
Flow Simulation . . . . . . . . . . . . 21--43
Scott A. Moe and
James A. Rossmanith and
David C. Seal Positivity-Preserving Discontinuous
Galerkin Methods with Lax--Wendroff Time
Discretizations . . . . . . . . . . . . 44--70
T. Pichard and
G. W. Alldredge and
S. Brull and
B. Dubroca and
M. Frank An Approximation of the $ M_2 $ Closure:
Application to Radiotherapy Dose
Simulation . . . . . . . . . . . . . . . 71--108
Qin Li and
Qilong Guo and
Dong Sun and
Pengxin Liu and
Hanxin Zhang A Fourth-Order Symmetric WENO Scheme
with Improved Performance by New Linear
and Nonlinear Optimizations . . . . . . 109--143
Wei Kang and
Lucas C. Wilcox Solving $1$D Conservation Laws Using
Pontryagin's Minimum Principle . . . . . 144--165
Andrea Perrotta and
Bernardo Favini A Second-Order Finite-Volume Scheme for
Euler Equations: Kinetic Energy
Preserving and Staggering Effects . . . 166--194
Lunji Song and
Kaifang Liu and
Shan Zhao A Weak Galerkin Method with an
Over--Relaxed Stabilization for Low
Regularity Elliptic Problems . . . . . . 195--218
Siyang Wang and
Gunilla Kreiss Convergence of Summation-by-Parts Finite
Difference Methods for the Wave Equation 219--245
D. Zorío and
A. Baeza and
P. Mulet An Approximate Lax--Wendroff-Type
Procedure for High Order Accurate
Schemes for Hyperbolic Conservation Laws 246--273
Lei Li and
Xiaoqian Xu and
Saverio E. Spagnolie A Locally Gradient-Preserving
Reinitialization for Level Set Functions 274--302
Arbaz Khan and
Akhlaq Husain Exponentially Accurate Spectral Element
Method for Fourth Order Elliptic
Problems . . . . . . . . . . . . . . . . 303--328
Christine Bernardi and
Jad Dakroub and
Gihane Mansour and
Farah Rafei and
Toni Sayah Convergence Analysis of Two Numerical
Schemes Applied to a Nonlinear Elliptic
Problem . . . . . . . . . . . . . . . . 329--347
Verónica Anaya and
David Mora and
Carlos Reales and
Ricardo Ruiz-Baier Mixed Methods for a
Stream-Function-Vorticity Formulation of
the Axisymmetric Brinkman Equations . . 348--364
Jan Nordström A Roadmap to Well Posed and Stable
Problems in Computational Physics . . . 365--385
Santiago Badia and
Juan Vicente Gutiérrez-Santacreu Convergence to Suitable Weak Solutions
for a Finite Element Approximation of
the Navier--Stokes Equations with
Numerical Subgrid Scale Modeling . . . . 386--413
Jing-Mei Qiu and
Giovanni Russo A High Order Multi-Dimensional
Characteristic Tracing Strategy for the
Vlasov--Poisson System . . . . . . . . . 414--434
Daniel P. Robinson and
Rachael Tappenden A Flexible ADMM Algorithm for Big Data
Applications . . . . . . . . . . . . . . 435--467
Yao Sun Indirect Boundary Integral Equation
Method for the Cauchy Problem of the
Laplace Equation . . . . . . . . . . . . 469--498
Jiming Wu Vertex-Centered Linearity-Preserving
Schemes for Nonlinear Parabolic Problems
on Polygonal Grids . . . . . . . . . . . 499--524
Futao Zhang and
Yan Xu and
Falai Chen Discontinuous Galerkin Based
Isogeometric Analysis for Geometric
Flows and Applications in Geometric
Modeling . . . . . . . . . . . . . . . . 525--546
Abderrazek Karoui and
Ahmed Souabni Weighted Finite Fourier Transform
Operator: Uniform Approximations of the
Eigenfunctions, Eigenvalues Decay and
Behaviour . . . . . . . . . . . . . . . 547--570
Alfredo Cano and
Carlos Moreno Transformation Methods for the Numerical
Integration of Three-Dimensional
Singular Functions . . . . . . . . . . . 571--593
Hailong Guo and
Xu Yang Polynomial Preserving Recovery for High
Frequency Wave Propagation . . . . . . . 594--614
Hui Guo and
Fan Yu and
Yang Yang Local Discontinuous Galerkin Method for
Incompressible Miscible Displacement
Problem in Porous Media . . . . . . . . 615--633
Zhaoxiang Li and
Zhi-Qiang Wang and
Jianxin Zhou A New Augmented Singular Transform and
its Partial Newton-Correction Method for
Finding More Solutions . . . . . . . . . 634--659
Lueling Jia and
Huanzhen Chen and
Hong Wang Mixed-Type Galerkin Variational
Principle and Numerical Simulation for a
Generalized Nonlocal Elastic Model . . . 660--681
Rong Huang and
Delin Chu Computing Singular Value Decompositions
of Parameterized Matrices with Total
Nonpositivity to High Relative Accuracy 682--711
Wei Deng and
Ming-Jun Lai and
Zhimin Peng and
Wotao Yin Parallel Multi-Block ADMM with $ o(1 /
k) $ Convergence . . . . . . . . . . . . 712--736
Anne Gelb and
Guohui Song Detecting Edges from Non-uniform Fourier
Data Using Fourier Frames . . . . . . . 737--758
Hengfei Ding and
Changpin Li High-Order Numerical Algorithms for
Riesz Derivatives via Constructing New
Generating Functions . . . . . . . . . . 759--784
Zhiqiang Li and
Zongqi Liang and
Yubin Yan High-Order Numerical Methods for Solving
Time Fractional Partial Differential
Equations . . . . . . . . . . . . . . . 785--803
H. Alici and
J. Shen Highly Accurate Pseudospectral
Approximations of the Prolate Spheroidal
Wave Equation for Any Bandwidth
Parameter and Zonal Wavenumber . . . . . 804--821
Rongsan Chen and
Min Zou and
Li Xiao Entropy-TVD Scheme for the Shallow Water
Equations in One Dimension . . . . . . . 822--838
Hossain Chizari and
Farzad Ismail A Grid-Insensitive LDA Method on
Triangular Grids Solving the System of
Euler Equations . . . . . . . . . . . . 839--874
B. Lee and
M. Kang and
S. Kim An Essentially Non-oscillatory
Crank--Nicolson Procedure for the
Simulation of Convection-Dominated Flows 875--895
Chunmei Wang and
Haomin Zhou A Weak Galerkin Finite Element Method
for a Type of Fourth Order Problem
Arising from Fluorescence Tomography . . 897--918
Sandra May and
Marsha Berger An Explicit Implicit Scheme for Cut
Cells in Embedded Boundary Meshes . . . 919--943
David I. Ketcheson and
Lajos Lóczi and
Aliya Jangabylova and
Adil Kusmanov Dense Output for Strong Stability
Preserving Runge--Kutta Methods . . . . 944--958
Yingda Cheng and
Andrew J. Christlieb and
Wei Guo and
Benjamin Ong An Asymptotic Preserving Maxwell Solver
Resulting in the Darwin Limit of
Electrodynamics . . . . . . . . . . . . 959--993
Maojun Li and
Philippe Guyenne and
Fengyan Li and
Liwei Xu A Positivity-Preserving Well-Balanced
Central Discontinuous Galerkin Method
for the Nonlinear Shallow Water
Equations . . . . . . . . . . . . . . . 994--1034
Xiao-Yan Liu and
C. S. Chen and
Andreas Karageorghis Conformal Mapping for the Efficient
Solution of Poisson Problems with the
Kansa--RBF Method . . . . . . . . . . . 1035--1061
Praveen Chandrashekar and
Markus Zenk Well-Balanced Nodal Discontinuous
Galerkin Method for Euler Equations with
Gravity . . . . . . . . . . . . . . . . 1062--1093
Weizhu Bao and
Yongyong Cai and
Xiaowei Jia and
Qinglin Tang Numerical Methods and Comparison for the
Dirac Equation in the Nonrelativistic
Limit Regime . . . . . . . . . . . . . . 1094--1134
Sigrun Ortleb A Kinetic Energy Preserving DG Scheme
Based on Gauss--Legendre Points . . . . 1135--1168
Thomas Carraro and
Christian Goll A Goal-Oriented Error Estimator for a
Class of Homogenization Problems . . . . 1169--1196
Habibullah Amin Chowdhury and
Adam Wittek and
Karol Miller and
Grand Roman Joldes An Element Free Galerkin Method Based on
the Modified Moving Least Squares
Approximation . . . . . . . . . . . . . 1197--1211
Benjamin W. Ong and
Andrew J. Christlieb and
Bryan D. Quaife A New Family of Regularized Kernels for
the Harmonic Oscillator . . . . . . . . 1212--1237
Qiao Wang and
Wei Zhou and
Yonggang Cheng and
Gang Ma and
Xiaolin Chang and
Qiang Huang The Boundary Element Method with a Fast
Multipole Accelerated Integration
Technique for $3$D Elastostatic Problems
with Arbitrary Body Forces . . . . . . . 1238--1264
Sergio Amat and
Juan Ruiz New WENO Smoothness Indicators
Computationally Efficient in the
Presence of Corner Discontinuities . . . 1265--1302
Hyun Geun Lee and
Jaemin Shin and
June-Yub Lee A Second-Order Operator Splitting
Fourier Spectral Method for Models of
Epitaxial Thin Film Growth . . . . . . . 1303--1318
Min Hyung Cho and
Wei Cai Efficient and Accurate Computation of
Electric Field Dyadic Green's Function
in Layered Media . . . . . . . . . . . . 1319--1350
Behrouz Parsa Moghaddam and
José António Tenreiro Machado Extended Algorithms for Approximating
Variable Order Fractional Derivatives
with Applications . . . . . . . . . . . 1351--1374
Ricardo Costa and
Stéphane Clain and
Gaspar J. Machado and
Raphaël Loub\`ere A Very High-Order Accurate Staggered
Finite Volume Scheme for the Stationary
Incompressible Navier--Stokes and Euler
Equations on Unstructured Meshes . . . . 1375--1411
Gang Pang and
Yibo Yang and
Shaoqiang Tang Exact Boundary Condition for
Semi-discretized Schrödinger Equation and
Heat Equation in a Rectangular Domain 1--13
T. I. Lakoba Long-Time Simulations of Nonlinear
Schrödinger-Type Equations using Step
Size Exceeding Threshold of Numerical
Instability . . . . . . . . . . . . . . 14--48
P. Gatto and
J. S. Hesthaven Efficient Preconditioning of hp-FEM
Matrices by Hierarchical Low-Rank
Approximations . . . . . . . . . . . . . 49--80
Jörg Stiller Nonuniformly Weighted Schwarz Smoothers
for Spectral Element Multigrid . . . . . 81--96
Harri Hakula and
Michael Neilan and
Jeffrey S. Ovall A Posteriori Estimates Using Auxiliary
Subspace Techniques . . . . . . . . . . 97--127
N. Chalmers and
L. Krivodonova Spatial and Modal Superconvergence of
the Discontinuous Galerkin Method for
Linear Equations . . . . . . . . . . . . 128--146
Pietro Dell'Acqua and
Marco Donatelli and
Claudio Estatico and
Mariarosa Mazza Structure Preserving Preconditioners for
Image Deblurring . . . . . . . . . . . . 147--171
Myeongmin Kang and
Myungjoo Kang and
Miyoun Jung Total Generalized Variation Based
Denoising Models for Ultrasound Images 172--197
Christoph Reisinger and
Julen Rotaetxe Arto Boundary Treatment and Multigrid
Preconditioning for Semi-Lagrangian
Schemes Applied to
Hamilton--Jacobi--Bellman Equations . . 198--230
Shao-chun Chen and
Li-na Dong and
Ji-kun Zhao Uniformly Convergent Cubic Nonconforming
Element For Darcy--Stokes Problem . . . 231--251
Shuvam Sen and
Tony W. H. Sheu On the Development of a Nonprimitive
Navier--Stokes Formulation Subject to
Rigorous Implementation of a New
Vorticity Integral Condition . . . . . . 252--290
Jian-Guo Liu and
Zheng Ma and
Zhennan Zhou Explicit and Implicit TVD Schemes for
Conservation Laws with Caputo
Derivatives . . . . . . . . . . . . . . 291--313
David A. Kopriva and
Jan Nordström and
Gregor J. Gassner Error Boundedness of Discontinuous
Galerkin Spectral Element Approximations
of Hyperbolic Problems . . . . . . . . . 314--330
Hong Zhu and
Xiaowei Zhang and
Delin Chu and
Li-Zhi Liao Nonconvex and Nonsmooth Optimization
with Generalized Orthogonality
Constraints: an Approximate Augmented
Lagrangian Method . . . . . . . . . . . 331--372
Patricio Farrell and
Alexander Linke Uniform Second Order Convergence of a
Complete Flux Scheme on Unstructured
$1$D Grids for a Singularly Perturbed
Advection--Diffusion Equation and Some
Multidimensional Extensions . . . . . . 373--395
Davide Forti and
Martina Bukac and
Annalisa Quaini and
Suncica Canic and
Simone Deparis A Monolithic Approach to
Fluid--Composite Structure Interaction 396--421
Weiping Bu and
Aiguo Xiao and
Wei Zeng Finite Difference/Finite Element Methods
for Distributed-Order Time Fractional
Diffusion Equations . . . . . . . . . . 422--441
Jooyoung Hahn and
Karol Mikula and
Peter Frolkovic and
Branislav Basara Inflow-Based Gradient Finite Volume
Method for a Propagation in a Normal
Direction in a Polyhedron Mesh . . . . . 442--465
Changfeng Li and
Yirang Yuan and
Tongjun Sun and
Qing Yang Mixed Volume Element-Characteristic
Fractional Step Difference Method for
Contamination from Nuclear Waste
Disposal . . . . . . . . . . . . . . . . 467--499
Geng Zhang and
Dan Cai and
Yong Du Improved ADI Scheme for Linear
Hyperbolic Equations: Extension to
Nonlinear Cases and Compact ADI Schemes 500--521
Zhi-Gang Jia and
Musheng Wei A New TV--Stokes Model for Image
Deblurring and Denoising with Fast
Algorithms . . . . . . . . . . . . . . . 522--541
Ceren Gürkan and
Martin Kronbichler and
Sonia Fernández-Méndez eXtended Hybridizable Discontinuous
Galerkin with Heaviside Enrichment for
Heat Bimaterial Problems . . . . . . . . 542--567
Vincent J. Ervin and
Thomas Führer and
Norbert Heuer and
Michael Karkulik DPG Method with Optimal Test Functions
for a Fractional Advection Diffusion
Equation . . . . . . . . . . . . . . . . 568--585
Hehu Xie and
Xinming Wu A Multilevel Correction Method for
Interior Transmission Eigenvalue Problem 586--604
Yifu Song and
Yushun Wang Energy-Preserving Algorithms for the
Benjamin Equation . . . . . . . . . . . 605--622
Wasilij Barsukow and
Philipp V. F. Edelmann and
Christian Klingenberg and
Fabian Miczek and
Friedrich K. Röpke A Numerical Scheme for the Compressible
Low-Mach Number Regime of Ideal Fluid
Dynamics . . . . . . . . . . . . . . . . 623--646
Chuan-Li Wang and
Zhong-Qing Wang and
Hong-Li Jia An hp-version Spectral Collocation
Method for Nonlinear Volterra
Integro-differential Equation with
Weakly Singular Kernels . . . . . . . . 647--678
Chao Zhang and
Dong-qin Gu and
Zhong-qing Wang and
Hui-yuan Li Efficient Space--Time Spectral Methods
for Second-Order Problems on Unbounded
Domains . . . . . . . . . . . . . . . . 679--699
Yangyang Xu and
Wotao Yin A Globally Convergent Algorithm for
Nonconvex Optimization Based on Block
Coordinate Update . . . . . . . . . . . 700--734
Christophe Besse and
Feng Xing Domain Decomposition Algorithms for Two
Dimensional Linear Schrödinger Equation 735--760
Waixiang Cao and
Qiumei Huang Superconvergence of Local Discontinuous
Galerkin Methods for Partial
Differential Equations with Higher Order
Derivatives . . . . . . . . . . . . . . 761--791
Yao Cheng and
Qiang Zhang Local Analysis of the Local
Discontinuous Galerkin Method with
Generalized Alternating Numerical Flux
for One-Dimensional Singularly Perturbed
Problem . . . . . . . . . . . . . . . . 792--819
Wei Gong and
Hehu Xie and
Ningning Yan Adaptive Multilevel Correction Method
for Finite Element Approximations of
Elliptic Optimal Control Problems . . . 820--841
Shu-Lin Wu Optimized Overlapping Schwarz Waveform
Relaxation for a Class of
Time-Fractional Diffusion Problems . . . 842--862
Xiaoli Li and
Hongxing Rui A Two-Grid Block-Centered Finite
Difference Method for the Nonlinear
Time-Fractional Parabolic Equation . . . 863--891
Dongfang Li and
Jilu Wang Unconditionally Optimal Error Analysis
of Crank--Nicolson Galerkin FEMs for a
Strongly Nonlinear Parabolic System . . 892--915
Jincheng Ren and
Xiaonian Long and
Shipeng Mao and
Jiwei Zhang Superconvergence of Finite Element
Approximations for the Fractional
Diffusion-Wave Equation . . . . . . . . 917--935
Xue Jiang and
Peijun Li and
Junliang Lv and
Weiying Zheng An Adaptive Finite Element Method for
the Wave Scattering with Transparent
Boundary Condition . . . . . . . . . . . 936--956
Xian-Ming Gu and
Ting-Zhu Huang and
Cui-Cui Ji and
Bruno Carpentieri and
Anatoly A. Alikhanov Fast Iterative Method with a
Second-Order Implicit Difference Scheme
for Time--Space Fractional
Convection--Diffusion Equation . . . . . 957--985
Caterina Bigoni and
Jan S. Hesthaven Adaptive WENO Methods Based on Radial
Basis Function Reconstruction . . . . . 986--1020
Yujie Zhu and
Zhensheng Sun and
Yuxin Ren and
Yu Hu and
Shiying Zhang A Numerical Strategy for Freestream
Preservation of the High Order Weighted
Essentially Non-oscillatory Schemes on
Stationary Curvilinear Grids . . . . . . 1021--1048
Carlos García and
Gabriel N. Gatica and
Salim Meddahi A New Mixed Finite Element Method for
Elastodynamics with Weak Symmetry . . . 1049--1079
Jean-Piero Suarez and
Gustaaf B. Jacobs Regularization of Singularities in the
Weighted Summation of Dirac-Delta
Functions for the Spectral Solution of
Hyperbolic Conservation Laws . . . . . . 1080--1092
Dongyang Shi and
Junjun Wang Unconditional Superconvergence Analysis
of a Crank--Nicolson Galerkin FEM for
Nonlinear Schrödinger Equation . . . . . 1093--1118
Li Luo and
Qian Zhang and
Xiao-Ping Wang and
Xiao-Chuan Cai A Parallel Finite Element Method for
$3$D Two-Phase Moving Contact Line
Problems in Complex Domains . . . . . . 1119--1145
Xi Deng and
Ziyao Sun and
Bin Xie and
Kensuke Yokoi and
Chungang Chen and
Feng Xiao A Non-oscillatory Multi-Moment Finite
Volume Scheme with Boundary Gradient
Switching . . . . . . . . . . . . . . . 1146--1168
Daniel Baffet and
Jan S. Hesthaven High-Order Accurate Adaptive Kernel
Compression Time-Stepping Schemes for
Fractional Differential Equations . . . 1169--1195
Daniel Peterseim and
Mira Schedensack Relaxing the CFL Condition for the Wave
Equation on Adaptive Meshes . . . . . . 1196--1213
Tianliang Hou and
Tao Tang and
Jiang Yang Numerical Analysis of Fully Discretized
Crank--Nicolson Scheme for
Fractional-in-Space Allen--Cahn
Equations . . . . . . . . . . . . . . . 1214--1231
R. Abgrall and
Q. Viville and
H. Beaugendre and
C. Dobrzynski Construction of a $p$-Adaptive
Continuous Residual Distribution Scheme 1232--1268
Huadong Gao and
Dongdong He Linearized Conservative Finite Element
Methods for the Nernst--Planck--Poisson
Equations . . . . . . . . . . . . . . . 1269--1289
Janis Bajars and
David J. Chappell and
Timo Hartmann and
Gregor Tanner Improved Approximation of Phase-Space
Densities on Triangulated Domains Using
Discrete Flow Mapping with
$p$-Refinement . . . . . . . . . . . . . 1290--1312
Xiaohao Cai and
Raymond Chan and
Mila Nikolova and
Tieyong Zeng A Three-Stage Approach for Segmenting
Degraded Color Images: Smoothing,
Lifting and Thresholding (SLaT) . . . . 1313--1332
Heike Benninghoff and
Harald Garcke Segmentation of Three-Dimensional Images
with Parametric Active Surfaces and
Topology Changes . . . . . . . . . . . . 1333--1367
Xiliang Lu and
Lijuan Wang and
Qishu Yan Computation of Time Optimal Control
Problems Governed by Linear Ordinary
Differential Equations . . . . . . . . . 1--25
Kai Fu and
Dong Liang The Time Second Order Mass Conservative
Characteristic FDM for
Advection--Diffusion Equations in High
Dimensions . . . . . . . . . . . . . . . 26--49
Yanni Gao and
Yonghai Li A Mortar Mixed Finite Volume Method for
Elliptic Problems on Non-matching
Multi-block Triangular Grids . . . . . . 50--69
Hongxing Rui and
Hao Pan A Block--Centered Finite Difference
Method for Slightly Compressible
Darcy--Forchheimer Flow in Porous Media 70--92
Guang-hua Gao and
Anatoly A. Alikhanov and
Zhi-zhong Sun The Temporal Second Order Difference
Schemes Based on the Interpolation
Approximation for Solving the Time
Multi-term and Distributed-Order
Fractional Sub-diffusion Equations . . . 93--121
Ryosuke Yano Kinetic Modeling of Local Epidemic
Spread and Its Simulation . . . . . . . 122--156
Giuseppe Pitton and
Gianluigi Rozza On the Application of Reduced Basis
Methods to Bifurcation Problems in
Incompressible Fluid Dynamics . . . . . 157--177
Souvik Roy and
Alfio Borz\`\i Numerical Investigation of a Class of
Liouville Control Problems . . . . . . . 178--202
Mei-Heng Yueh and
Wen-Wei Lin and
Chin-Tien Wu and
Shing-Tung Yau An Efficient Energy Minimization for
Conformal Parameterizations . . . . . . 203--227
D. J. Liu and
D. D. Jiang and
Y. Liu and
Q. Q. Xia Stabilized FEM for Some Optimal Design
Problem . . . . . . . . . . . . . . . . 228--241
Houde Han and
Yintzer Shih and
Dongsheng Yin Tailored Finite Point Methods for
Solving Singularly Perturbed Eigenvalue
Problems with Higher Eigenvalues . . . . 242--282
Xu-hong Yu and
Ben-yu Guo Spectral Method for Vorticity-Stream
Function Form of Navier--Stokes
Equations in an Infinite Channel with
Slip Boundary Conditions . . . . . . . . 283--302
Xinming Wu and
Zaiwen Wen and
Weizhu Bao A Regularized Newton Method for
Computing Ground States of
Bose--Einstein Condensates . . . . . . . 303--329
Johnny Guzmán and
Manuel A. Sánchez and
Marcus Sarkis A Finite Element Method for
High-Contrast Interface Problems with
Error Estimates Independent of Contrast 330--365
Freekjan Brink and
Ferenc Izsák and
J. J. W. van der Vegt Hamiltonian Finite Element
Discretization for Nonlinear Free
Surface Water Waves . . . . . . . . . . 366--394
Zhaopeng Hao and
Wanrong Cao An Improved Algorithm Based on Finite
Difference Schemes for Fractional
Boundary Value Problems with Nonsmooth
Solution . . . . . . . . . . . . . . . . 395--415
Dominique Zosso and
Braxton Osting and
Mandy (Mengqi) Xia and
Stanley J. Osher An Efficient Primal--Dual Method for the
Obstacle Problem . . . . . . . . . . . . 416--437
Haitao Leng and
Yanping Chen Convergence and Quasi-Optimality of an
Adaptive Finite Element Method for
Optimal Control Problems on $ L^2 $
Errors . . . . . . . . . . . . . . . . . 438--458
Sigal Gottlieb and
Johnny Guzmán and
Fengyan Li and
Jennifer K. Ryan Special Issue in Honor of Professor
Chi-Wang Shu . . . . . . . . . . . . . . 459--460
R. Abgrall High Order Schemes for Hyperbolic
Problems Using Globally Continuous
Approximation and Avoiding Mass Matrices 461--494
Susanne C. Brenner and
Jiguang Sun and
Li-yeng Sung Hodge Decomposition Methods for a
Quad-Curl Problem on Planar Domains . . 495--513
Xiaofeng Cai and
Wei Guo and
Jing-Mei Qiu A High Order Conservative
Semi-Lagrangian Discontinuous Galerkin
Method for Two-Dimensional Transport
Simulations . . . . . . . . . . . . . . 514--542
Waixiang Cao and
Xu Zhang and
Zhimin Zhang and
Qingsong Zou Superconvergence of Immersed Finite
Volume Methods for One-Dimensional
Interface Problems . . . . . . . . . . . 543--565
Zheng Chen and
Liu Liu and
Lin Mu DG-IMEX Stochastic Galerkin Schemes for
Linear Transport Equation with Random
Inputs and Diffusive Scalings . . . . . 566--592
Ching-Shan Chou and
Weizhou Sun and
Yulong Xing and
He Yang Local Discontinuous Galerkin Methods for
the Khokhlov--Zabolotskaya--Kuznetzov
Equation . . . . . . . . . . . . . . . . 593--616
Yat Tin Chow and
Jérôme Darbon and
Stanley Osher and
Wotao Yin Algorithm for Overcoming the Curse of
Dimensionality For Time-Dependent
Non-convex Hamilton--Jacobi Equations
Arising From Optimal Control and
Differential Games Problems . . . . . . 617--643
Bernardo Cockburn and
Zhu Wang Adjoint-Based, Superconvergent Galerkin
Approximations of Linear Functionals . . 644--666
Sidafa Conde and
Sigal Gottlieb and
Zachary J. Grant and
John N. Shadid Implicit and Implicit--Explicit Strong
Stability Preserving Runge--Kutta
Methods with High Linear Order . . . . . 667--690
A. Ditkowski and
S. Gottlieb Error Inhibiting Block One-step Schemes
for Ordinary Differential Equations . . 691--711
Bo Dong Optimally Convergent HDG Method for
Third-Order Korteweg--de Vries Type
Equations . . . . . . . . . . . . . . . 712--735
Zhen Gao and
Xiao Wen and
Wai Sun Don Enhanced Robustness of the Hybrid
Compact--WENO Finite Difference Scheme
for Hyperbolic Conservation Laws with
Multi-resolution Analysis and Tukey's
Boxplot Method . . . . . . . . . . . . . 736--752
Gerardo Hernandez-Duenas A Hybrid Method to Solve Shallow Water
Flows with Horizontal Density Gradients 753--782
Yifeng Hou and
Roger Temam About the Modeling of the Indentation of
a Virus Shell: The Role of the Shape of
the Probe . . . . . . . . . . . . . . . 783--796
Jingwei Hu and
Xiangxiong Zhang On a Class of Implicit--Explicit
Runge--Kutta Schemes for Stiff Kinetic
Equations Preserving the Navier--Stokes
Limit . . . . . . . . . . . . . . . . . 797--818
Antony Jameson Evaluation of Fully Implicit
Runge--Kutta Schemes for Unsteady Flow
Calculations . . . . . . . . . . . . . . 819--852
Jiahua Jiang and
Yanlai Chen and
Akil Narayan Offline-Enhanced Reduced Basis Method
Through Adaptive Construction of the
Surrogate Training Set . . . . . . . . . 853--875
Arbaz Khan and
Pravir Dutt and
Chandra Shekhar Upadhyay Spectral Element Method for Parabolic
Initial Value Problem with Non-Smooth
Data: Analysis and Application . . . . . 876--905
Christian Klingenberg and
Gero Schnücke and
Yinhua Xia An Arbitrary Lagrangian--Eulerian Local
Discontinuous Galerkin Method for
Hamilton--Jacobi Equations . . . . . . . 906--942
Xingjie Helen Li and
Chi-Wang Shu and
Yang Yang Local Discontinuous Galerkin Method for
the Keller--Segel Chemotaxis Model . . . 943--967
Zhilin Li and
Fangfang Qin An Augmented Method for 4th Order PDEs
with Discontinuous Coefficients . . . . 968--979
Dong Lu and
Yong-Tao Zhang Computational Complexity Study on Krylov
Integration Factor WENO Method for High
Spatial Dimension Convection--Diffusion
Problems . . . . . . . . . . . . . . . . 980--1027
Yuan Liu and
Yingda Cheng and
Chi-Wang Shu A Simple Bound-Preserving Sweeping
Technique for Conservative Numerical
Approximations . . . . . . . . . . . . . 1028--1071
Mahsa Mirzargar and
Ashok Jallepalli and
Jennifer K. Ryan and
Robert M. Kirby Hexagonal Smoothness-Increasing
Accuracy-Conserving Filtering . . . . . 1072--1093
Philip Roe Is Discontinuous Reconstruction Really a
Good Idea? . . . . . . . . . . . . . . . 1094--1114
J. Romero and
F. D. Witherden and
A. Jameson A Direct Flux Reconstruction Scheme for
Advection--Diffusion Problems on
Triangular Grids . . . . . . . . . . . . 1115--1144
Jochen Schütz and
David C. Seal and
Alexander Jaust Implicit Multiderivative Collocation
Solvers for Linear Partial Differential
Equations with Discontinuous Galerkin
Spatial Discretizations . . . . . . . . 1145--1163
Zuoqiang Shi and
Stanley Osher and
Wei Zhu Weighted Nonlocal Laplacian on
Interpolation from Sparse Data . . . . . 1164--1177
Huailing Song and
Chi-Wang Shu Unconditional Energy Stability Analysis
of a Second Order Implicit--Explicit
Local Discontinuous Galerkin Method for
the Cahn--Hilliard Equation . . . . . . 1178--1203
Christopher J. Vogl and
Randall J. LeVeque A High-Resolution Finite Volume Seismic
Model to Generate Seafloor Deformation
for Tsunami Modeling . . . . . . . . . . 1204--1215
He Yang and
Fengyan Li Discontinuous Galerkin Methods for
Relativistic Vlasov--Maxwell System . . 1216--1248
Fan Yu and
Hui Guo and
Nattaporn Chuenjarern and
Yang Yang Conservative Local Discontinuous
Galerkin Method for Compressible
Miscible Displacements in Porous Media 1249--1275
Mengping Zhang and
Jue Yan Fourier Type Super Convergence Study on
DDGIC and Symmetric DDG Methods . . . . 1276--1289
Lingling Zhou and
Yan Xu and
Zhimin Zhang and
Waixiang Cao Superconvergence of Local Discontinuous
Galerkin Method for One-Dimensional
Linear Schrödinger Equations . . . . . . 1290--1315
Hongqiang Zhu and
Jianxian Qiu and
Jing-Mei Qiu An $h$-Adaptive RKDG Method for the
Two-Dimensional Incompressible Euler
Equations and the Guiding Center Vlasov
Model . . . . . . . . . . . . . . . . . 1316--1337
Jun Zhu and
Jianxian Qiu A New Type of Finite Volume WENO Schemes
for Hyperbolic Conservation Laws . . . . 1338--1359
Roberto Cavoretto and
Alessandra De Rossi and
Emma Perracchione Optimal Selection of Local Approximants
in RBF--PU Interpolation . . . . . . . . 1--22
Chunjia Bi and
Cheng Wang and
Yanping Lin A Posteriori Error Estimates of Two-Grid
Finite Element Methods for Nonlinear
Elliptic Problems . . . . . . . . . . . 23--48
Zhiqiang Zhou and
Jingtang Ma and
Hai-wei Sun Fast Laplace Transform Methods for
Free-Boundary Problems of Fractional
Diffusion Equations . . . . . . . . . . 49--69
Guoqiao You and
Shingyu Leung Eulerian Based Interpolation Schemes for
Flow Map Construction and Line Integral
Computation with Applications to
Lagrangian Coherent Structures
Extraction . . . . . . . . . . . . . . . 70--96
Shi Jin and
Zheng Ma The Discrete Stochastic Galerkin Method
for Hyperbolic Equations with Non-smooth
and Random Coefficients . . . . . . . . 97--121
Changna Lu and
Weizhang Huang and
Jianxian Qiu An Adaptive Moving Mesh Finite Element
Solution of the Regularized Long Wave
Equation . . . . . . . . . . . . . . . . 122--144
Iain Smears Nonoverlapping Domain Decomposition
Preconditioners for Discontinuous
Galerkin Approximations of
Hamilton--Jacobi--Bellman Equations . . 145--174
Ke Yin and
Xue-Cheng Tai An Effective Region Force for Some
Variational Models for Learning and
Clustering . . . . . . . . . . . . . . . 175--196
Immanuel Martini and
Bernard Haasdonk and
Gianluigi Rozza Certified Reduced Basis Approximation
for the Coupling of Viscous and Inviscid
Parametrized Flow Models . . . . . . . . 197--219
Hongfei Fu and
Hong Wang and
Zhu Wang POD/DEIM Reduced-Order Modeling of
Time-Fractional Partial Differential
Equations with Applications in Parameter
Identification . . . . . . . . . . . . . 220--243
Imre Fekete and
David I. Ketcheson and
Lajos Lóczi Positivity for Convective
Semi-discretizations . . . . . . . . . . 244--266
Roberto Cavoretto and
Teseo Schneider and
Patrick Zulian OpenCL Based Parallel Algorithm for
RBF--PUM Interpolation . . . . . . . . . 267--289
N. Anders Petersson and
Björn Sjögreen High Order Accurate Finite Difference
Modeling of Seismo--Acoustic Wave
Propagation in a Moving Atmosphere and a
Heterogeneous Earth Model Coupled Across
a Realistic Topography . . . . . . . . . 290--323
Zhaoliang Meng and
Jintao Cui and
Zhongxuan Luo A New Rotated Nonconforming
Quadrilateral Element . . . . . . . . . 324--335
Zhenning Cai and
Manuel Torrilhon Numerical Simulation of Microflows Using
Moment Methods with Linearized Collision
Operator . . . . . . . . . . . . . . . . 336--374
Nabil Chaabane and
Béatrice Rivi\`ere A Sequential Discontinuous Galerkin
Method for the Coupling of Flow and
Geomechanics . . . . . . . . . . . . . . 375--395
Jian Huang and
Long Chen and
Hongxing Rui Multigrid Methods for a Mixed Finite
Element Method of the Darcy--Forchheimer
Model . . . . . . . . . . . . . . . . . 396--411
Ze-Jia Xie and
Xiao-Qing Jin and
Yi-Min Wei Tensor Methods for Solving Symmetric $
{\mathcal {M}}$-tensor Systems . . . . . 412--425
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Error Analysis of Projection Methods for
Non inf-sup Stable Mixed Finite
Elements: The Navier--Stokes Equations 426--455
Francisco Durango and
Julia Novo Two-Grid Mixed Finite-Element
Approximations to the Navier--Stokes
Equations Based on a Newton-Type Step 456--473
Shidong Jiang and
Dong Wang and
Xiao-Ping Wang An Efficient Boundary Integral Scheme
for the MBO Threshold Dynamics Method
via the NUFFT . . . . . . . . . . . . . 474--490
Sebastian Minjeaud and
Richard Pasquetti High Order $ C^0 $-Continuous Galerkin
Schemes for High Order PDEs,
Conservation of Quadratic Invariants and
Application to the Korteweg--de Vries
Model . . . . . . . . . . . . . . . . . 491--518
Samir Karaa and
Kassem Mustapha and
Amiya K. Pani Optimal Error Analysis of a FEM for
Fractional Diffusion Problems by Energy
Arguments . . . . . . . . . . . . . . . 519--535
Nianyu Yi and
Yunqing Huang and
Wei Yang Function, Derivative and High-Order
Derivatives Recovery Methods Using the
Local Symmetry Projection . . . . . . . 536--572
O. Karakashian and
C. Collins Two-Level Additive Schwarz Methods for
Discontinuous Galerkin Approximations of
the Biharmonic Equation . . . . . . . . 573--604
Waixiang Cao and
Xu Zhang and
Zhimin Zhang and
Qingsong Zou Correction to: Superconvergence of
Immersed Finite Volume Methods for
One-Dimensional Interface Problems . . . 605--605
Chang Ho Kim and
Kwang-Il You and
Youngsoo Ha Hybrid Finite Difference Weighted
Essentially Non-oscillatory Schemes for
the Compressible Ideal
Magnetohydrodynamics Equation . . . . . 607--630
Jiwon Seo and
Seung-yeal Ha and
Chohong Min Convergence Analysis in the Maximum Norm
of the Numerical Gradient of the
Shortley--Weller Method . . . . . . . . 631--639
Peng Li and
Wai-Sun Don and
Cheng Wang and
Zhen Gao High Order Positivity- and
Bound-Preserving Hybrid Compact-WENO
Finite Difference Scheme for the
Compressible Euler Equations . . . . . . 640--666
Tomás Chacón Rebollo and
Macarena Gómez Mármol and
Frédéric Hecht and
Samuele Rubino and
Isabel Sánchez Muñoz A High-Order Local Projection
Stabilization Method for Natural
Convection Problems . . . . . . . . . . 667--692
Rui Li and
Yali Gao and
Jian Li and
Zhangxin Chen Discontinuous Finite Volume Element
Method for a Coupled Non-stationary
Stokes--Darcy Problem . . . . . . . . . 693--727
Zhengguang Liu and
Xiaoli Li A Fast Finite Difference Method for a
Continuous Static Linear Bond-Based
Peridynamics Model of Mechanics . . . . 728--742
Jin-Jin Mei and
Yiqiu Dong and
Ting-Zhu Huang and
Wotao Yin Cauchy Noise Removal by Nonconvex ADMM
with Convergence Guarantees . . . . . . 743--766
Yifei Lou and
Ming Yan Fast $ L_1 $--$ L_2 $ Minimization via a
Proximal Operator . . . . . . . . . . . 767--785
Alessandro Buccini and
Marco Donatelli and
Fabio Ferri Weakly Constrained Lucy--Richardson with
Applications to Inversion of Light
Scattering Data . . . . . . . . . . . . 786--804
Riccardo Zamolo and
Lucia Parussini and
Valentino Pediroda Distributed Lagrange Multiplier
Functions for Fictitious Domain Method
with Spectral/$ h p $ Element
Discretization . . . . . . . . . . . . . 805--825
Min Tao and
Xiaoming Yuan On the Optimal Linear Convergence Rate
of a Generalized Proximal Point
Algorithm . . . . . . . . . . . . . . . 826--850
Ruonan Shi and
Jae-Hun Jung A Domain Decomposition Fourier
Continuation Method for Enhanced $ L_1 $
Regularization Using Sparsity of Edges
in Reconstructing Fourier Data . . . . . 851--871
Thomas Dunst and
Andreas Prohl Stochastic Optimal Control of Finite
Ensembles of Nanomagnets . . . . . . . . 872--894
Markus Huber and
Ulrich Rüde and
Christian Waluga and
Barbara Wohlmuth Surface Couplings for Subdomain-Wise
Isoviscous Gradient Based Stokes Finite
Element Discretizations . . . . . . . . 895--919
Xiaojun Tang and
Yang Shi and
Heyong Xu Well Conditioned Pseudospectral Schemes
with Tunable Basis for Fractional Delay
Differential Equations . . . . . . . . . 920--936
Jean Daniel Mukam and
Antoine Tambue Strong Convergence Analysis of the
Stochastic Exponential Rosenbrock Scheme
for the Finite Element Discretization of
Semilinear SPDEs Driven by
Multiplicative and Additive Noise . . . 937--978
Rong An and
Jian Su Optimal Error Estimates of Semi-implicit
Galerkin Method for Time-Dependent
Nematic Liquid Crystal Flows . . . . . . 979--1008
Meng Zhao and
Hong Wang and
Aijie Cheng A Fast Finite Difference Method for
Three-Dimensional Time-Dependent
Space-Fractional Diffusion Equations
with Fractional Derivative Boundary
Conditions . . . . . . . . . . . . . . . 1009--1033
Minghua Chen and
Weihua Deng and
Stefano Serra-Capizzano Uniform Convergence of $V$-cycle
Multigrid Algorithms for Two-Dimensional
Fractional Feynman--Kac Equation . . . . 1034--1059
Maryam Ghasemi and
Hermann J. Eberl Time Adaptive Numerical Solution of a
Highly Degenerate Diffusion--Reaction
Biofilm Model Based on Regularisation 1060--1090
Tingting Meng and
Lijun Yi An $h$--$p$ Version of the Continuous
Petrov--Galerkin Method for Nonlinear
Delay Differential Equations . . . . . . 1091--1114
Xiaoli Li and
Hongxing Rui Block-Centered Finite Difference Method
for Simulating Compressible Wormhole
Propagation . . . . . . . . . . . . . . 1115--1145
Ruixue Zhao and
Jinyan Fan On a New Updating Rule of the
Levenberg--Marquardt Parameter . . . . . 1146--1162
Benjamin Ivorra Application of the Laminar
Navier--Stokes Equations for Solving
$2$D and $4$D Pathfinding Problems with
Static and Dynamic Spatial Constraints:
Implementation and Validation in Comsol
Multiphysics . . . . . . . . . . . . . . 1163--1187
Magnus Svärd and
Jan Nordström Response to ``Convergence of
Summation-by-Parts Finite Difference
Methods for the Wave Equation'' . . . . 1188--1192
Mohamed Addam and
Abderrahman Bouhamidi and
Mohammed Heyouni On Solving an Acoustic Wave Problem Via
Frequency--Domain Approach and Tensorial
Spline Galerkin Method . . . . . . . . . 1193--1220
Chengjian Zhang and
Cui Li Generalized Störmer-Cowell Methods for
Nonlinear BVPs of Second-Order
Delay--Integro-Differential Equations 1221--1240
Rongjie Lai and
Jia Li Manifold Based Low-Rank Regularization
for Image Restoration and
Semi-Supervised Learning . . . . . . . . 1241--1263
Quanling Deng and
Victor Ginting Locally Conservative Continuous Galerkin
FEM for Pressure Equation in Two--Phase
Flow Model in Subsurfaces . . . . . . . 1264--1285
Sheng Chen and
Jie Shen and
Li-Lian Wang Laguerre Functions and Their
Applications to Tempered Fractional
Differential Equations on Infinite
Intervals . . . . . . . . . . . . . . . 1286--1313
Wenrui Hao A Homotopy Method for Parameter
Estimation of Nonlinear Differential
Equations with Multiple Optima . . . . . 1314--1324
Youngjoon Hong and
Chang-Yeol Jung Enriched Spectral Method for Stiff
Convection--Dominated Equations . . . . 1325--1346
Xiao-Long Deng and
Maojun Li Simulating Compressible Two--Medium
Flows with Sharp--Interface Adaptive
Runge--Kutta Discontinuous Galerkin
Methods . . . . . . . . . . . . . . . . 1347--1368
Junping Wang and
Ruishu Wang and
Qilong Zhai and
Ran Zhang A Systematic Study on Weak Galerkin
Finite Element Methods for Second Order
Elliptic Problems . . . . . . . . . . . 1369--1396
Hailong Guo and
Zhimin Zhang and
Qingsong Zou A $ C^0 $ Linear Finite Element Method
for Biharmonic Problems . . . . . . . . 1397--1422
Siu Wun Cheung and
Eric Chung and
Hyea Hyun Kim A Mass Conservative Scheme for
Fluid--Structure Interaction Problems by
the Staggered Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 1423--1456
Jun Hu and
Limin Ma A Penalized Crouzeix--Raviart Element
Method for Second Order Elliptic
Eigenvalue Problems . . . . . . . . . . 1457--1479
Oliver Kolb A Third Order Hierarchical Basis WENO
Interpolation for Sparse Grids with
Application to Conservation Laws with
Uncertain Data . . . . . . . . . . . . . 1480--1503
T. S. Jang A New Functional Iterative Algorithm for
the Regularized Long--Wave Equation
Using an Integral Equation Formalism . . 1504--1532
Xiaofeng Yang Numerical Approximations for the
Cahn--Hilliard Phase Field Model of the
Binary Fluid--Surfactant System . . . . 1533--1553
Can Huang and
Zhimin Zhang and
Qingshuo Song Spectral Methods for Substantial
Fractional Differential Equations . . . 1554--1574
Lorenzo Pareschi and
Mattia Zanella Structure Preserving Schemes for
Nonlinear Fokker--Planck Equations and
Applications . . . . . . . . . . . . . . 1575--1600
Guillaume Latu and
Michel Mehrenberger and
Yaman Güçlü and
Maurizio Ottaviani and
Eric Sonnendrücker Field-Aligned Interpolation for
Semi-Lagrangian Gyrokinetic Simulations 1601--1650
Xiaobing Feng and
Michael Neilan and
Stefan Schnake Interior Penalty Discontinuous Galerkin
Methods for Second Order Linear
Non-divergence Form Elliptic PDEs . . . 1651--1676
Daniele A. Di Pietro and
Stella Krell A Hybrid High-Order Method for the
Steady Incompressible Navier--Stokes
Problem . . . . . . . . . . . . . . . . 1677--1705
Jie Shen and
Jie Xu and
Pingwen Zhang Approximations on $ {\rm SO}(3) $ by
Wigner $D$-matrix and Applications . . . 1706--1724
Dongho Kim and
Eun-Jae Park and
Boyoon Seo Space-Time Adaptive Methods for the
Mixed Formulation of a Linear Parabolic
Problem . . . . . . . . . . . . . . . . 1725--1756
Abhishek Sheshadri and
Antony Jameson An Analysis of Stability of the Flux
Reconstruction Formulation on
Quadrilateral Elements for the Linear
Advection--Diffusion Equation . . . . . 1757--1785
Wei Liu and
Jintao Cui A Two--Grid Block--Centered Finite
Difference Algorithm for Nonlinear
Compressible Darcy--Forchheimer Model in
Porous Media . . . . . . . . . . . . . . 1786--1815
Wen-Feng Huang and
Yu-Xin Ren and
Qiuju Wang and
Xiong Jiang High Resolution Finite Volume Scheme
Based on the Quintic Spline
Reconstruction on Non-uniform Grids . . 1816--1852
Jingya Chang and
Weiyang Ding and
Liqun Qi and
Hong Yan Computing the $p$-Spectral Radii of
Uniform Hypergraphs with Applications 1--25
Bilal Abbasi and
Adam M. Oberman Computing the Level Set Convex Hull . . 26--42
Shangqi Gao and
Qibin Fan A Mixture of Nuclear Norm and Matrix
Factorization for Tensor Completion . . 43--64
Xiaofeng Cai and
Jianxian Qiu and
Jingmei Qiu Finite Volume HWENO Schemes for
Nonconvex Conservation Laws . . . . . . 65--82
David C. Del Rey Fernández and
Jason E. Hicken and
David W. Zingg Simultaneous Approximation Terms for
Multi-dimensional Summation-by-Parts
Operators . . . . . . . . . . . . . . . 83--110
Irene Kyza and
Stephen Metcalfe and
Thomas P. Wihler hp-Adaptive Galerkin Time Stepping
Methods for Nonlinear Initial Value
Problems . . . . . . . . . . . . . . . . 111--127
Changfeng Xue and
Shaozhong Deng Recursive Computation of Logarithmic
Derivatives, Ratios, and Products of
Spheroidal Harmonics and Modified Bessel
Functions and Applications . . . . . . . 128--156
Jing An and
Zhimin Zhang An Efficient Spectral--Galerkin
Approximation and Error Analysis for
Maxwell Transmission Eigenvalue Problems
in Spherical Geometries . . . . . . . . 157--181
Wuchen Li and
Ernest K. Ryu and
Stanley Osher and
Wotao Yin and
Wilfrid Gangbo A Parallel Method for Earth Mover's
Distance . . . . . . . . . . . . . . . . 182--197
Bo Dong and
Matthew M. Lin and
Haesun Park Integer Matrix Approximation and Data
Mining . . . . . . . . . . . . . . . . . 198--224
Theresa Scarnati and
Anne Gelb and
Rodrigo B. Platte Using $ \ell_1 $ Regularization to
Improve Numerical Partial Differential
Equation Solvers . . . . . . . . . . . . 225--252
Lai Wang and
Meilin Yu Compact Direct Flux Reconstruction for
Conservation Laws . . . . . . . . . . . 253--275
Mark Kärcher and
Zoi Tokoutsi and
Martin A. Grepl and
Karen Veroy Certified Reduced Basis Methods for
Parametrized Elliptic Optimal Control
Problems with Distributed Controls . . . 276--307
Davide Modesti and
Sergio Pirozzoli An Efficient Semi-implicit Solver for
Direct Numerical Simulation of
Compressible Flows at All Speeds . . . . 308--331
Darae Jeong and
Junseok Kim A Projection Method for the Conservative
Discretizations of Parabolic Partial
Differential Equations . . . . . . . . . 332--349
Samuel Dubuis and
Marco Picasso An Adaptive Algorithm for the Time
Dependent Transport Equation with
Anisotropic Finite Elements and the
Crank--Nicolson Scheme . . . . . . . . . 350--375
Bernardo Cockburn and
Manuel A. Sánchez and
Chunguang Xiong Supercloseness of Primal--Dual Galerkin
Approximations for Second Order Elliptic
Problems . . . . . . . . . . . . . . . . 376--394
Inmaculada Higueras and
Teo Roldán Order Barrier for Low-Storage DIRK
Methods with Positive Weights . . . . . 395--404
Lorella Fatone and
Daniele Funaro Isospectral Domains for Discrete
Elliptic Operators . . . . . . . . . . . 405--426
Huangxin Chen and
Shuyu Sun and
Tao Zhang Energy Stability Analysis of Some Fully
Discrete Numerical Schemes for
Incompressible Navier--Stokes Equations
on Staggered Grids . . . . . . . . . . . 427--456
Haiyong Wang and
Lun Zhang Jacobi Polynomials on the Bernstein
Ellipse . . . . . . . . . . . . . . . . 457--477
Hanwool Na and
Myeongmin Kang and
Miyoun Jung and
Myungjoo Kang An Exp Model with Spatially Adaptive
Regularization Parameters for
Multiplicative Noise Removal . . . . . . 478--509
Ming Sun and
Jichun Li and
Peizhen Wang and
Zhimin Zhang Superconvergence Analysis of High-Order
Rectangular Edge Elements for
Time-Harmonic Maxwell's Equations . . . 510--535
Joshua Buli and
Yulong Xing Local Discontinuous Galerkin Methods for
the Boussinesq Coupled BBM System . . . 536--559
Matteo Giacomini An Equilibrated Fluxes Approach to the
Certified Descent Algorithm for Shape
Optimization Using Conforming Finite
Element and Discontinuous Galerkin
Discretizations . . . . . . . . . . . . 560--595
Bernardo Cockburn and
Zhixing Fu and
Allan Hungria and
Liangyue Ji and
Manuel A. Sánchez and
Francisco-Javier Sayas Stormer-Numerov HDG Methods for Acoustic
Waves . . . . . . . . . . . . . . . . . 597--624
Lisl Weynans Super-Convergence in Maximum Norm of the
Gradient for the Shortley--Weller Method 625--637
Zuoqiang Shi and
Stanley Osher and
Wei Zhu Generalization of the Weighted Nonlocal
Laplacian in Low Dimensional Manifold
Model . . . . . . . . . . . . . . . . . 638--656
Lucas Friedrich and
David C. Del Rey Fernández and
Andrew R. Winters and
Gregor J. Gassner and
David W. Zingg and
Jason Hicken Conservative and Stable Degree
Preserving SBP Operators for
Non-conforming Meshes . . . . . . . . . 657--686
Cheng Zhang and
Jingfang Huang and
Cheng Wang and
Xingye Yue On the Operator Splitting and Integral
Equation Preconditioned Deferred
Correction Methods for the ``Good''
Boussinesq Equation . . . . . . . . . . 687--712
You-Wei Wen and
Wai-Ki Ching and
Michael Ng A Semi-smooth Newton Method for Inverse
Problem with Uniform Noise . . . . . . . 713--732
Duy-Minh Dang and
Luis Ortiz-Gracia A Dimension Reduction Shannon-Wavelet
Based Method for Option Pricing . . . . 733--761
M. Rachh and
T. Askham Integral Equation Formulation of the
Biharmonic Dirichlet Problem . . . . . . 762--781
Lin Mu and
Junping Wang and
Xiu Ye A Weak Galerkin Method for the
Reissner--Mindlin Plate in Primary Form 782--802
Ming-Jun Lai and
Chunmei Wang A Bivariate Spline Method for Second
Order Elliptic Equations in
Non-divergence Form . . . . . . . . . . 803--829
Philipp W. Schroeder and
Gert Lube Divergence-Free $H$ (div)-FEM for
Time-Dependent Incompressible Flows with
Applications to High Reynolds Number
Vortex Dynamics . . . . . . . . . . . . 830--858
Raz Z. Nossek and
Guy Gilboa Flows Generating Nonlinear
Eigenfunctions . . . . . . . . . . . . . 859--888
Youngmok Jeon Hybrid Spectral Difference Methods for
Elliptic Equations on Exterior Domains
with the Discrete Radial Absorbing
Boundary Condition . . . . . . . . . . . 889--905
Sofia Eriksson A Dual Consistent Finite Difference
Method with Narrow Stencil Second
Derivative Operators . . . . . . . . . . 906--940
Prabal Singh Verma and
Wolf-Christian Müller Higher Order Finite Volume Central
Schemes for Multi-dimensional Hyperbolic
Problems . . . . . . . . . . . . . . . . 941--969
Haotao Cai and
Yanping Chen A Fractional Order Collocation Method
for Second Kind Volterra Integral
Equations with Weakly Singular Kernels 970--992
Hongwei Li and
Lili Ju and
Chenfei Zhang and
Qiujin Peng Unconditionally Energy Stable Linear
Schemes for the Diffuse Interface Model
with Peng--Robinson Equation of State 993--1015
Wai Sun Don and
Bao-Shan Wang and
Zhen Gao Fast Iterative Adaptive Multi-quadric
Radial Basis Function Method for Edges
Detection of Piecewise Functions-I:
Uniform Mesh . . . . . . . . . . . . . . 1016--1039
Hendrik Ranocha and
Philipp Öffner $ L_2 $ Stability of Explicit
Runge--Kutta Schemes . . . . . . . . . . 1040--1056
Marcel Klinge and
Rüdiger Weiner Strong Stability Preserving Explicit
Peer Methods for Discontinuous Galerkin
Discretizations . . . . . . . . . . . . 1057--1078
Eric T. Chung and
Eun-Jae Park and
Lina Zhao Guaranteed A Posteriori Error Estimates
for a Staggered Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 1079--1101
Xue-lei Lin and
Michael K. Ng and
Hai-Wei Sun Stability and Convergence Analysis of
Finite Difference Schemes for
Time-Dependent Space--Fractional
Diffusion Equations with Variable
Diffusion Coefficients . . . . . . . . . 1102--1127
Chhanda Sen and
Harish Kumar Entropy Stable Schemes For Ten--Moment
Gaussian Closure Equations . . . . . . . 1128--1155
Xiaolong Long and
Knut Solna and
Jack Xin Three $ l_1 $ Based Nonconvex Methods in
Constructing Sparse Mean Reverting
Portfolios . . . . . . . . . . . . . . . 1156--1186
Omer San and
Prakash Vedula Generalized Deconvolution Procedure for
Structural Modeling of Turbulence . . . 1187--1206
Tao Zhao A Convergence Analysis of the Inexact
Simplified Jacobi--Davidson Algorithm
for Polynomial Eigenvalue Problems . . . 1207--1228
Rong Huang A Periodic $ q d$-Type Reduction for
Computing Eigenvalues of Structured
Matrix Products to High Relative
Accuracy . . . . . . . . . . . . . . . . 1229--1261
Juan Manzanero and
Gonzalo Rubio and
Esteban Ferrer and
Eusebio Valero and
David A. Kopriva Insights on Aliasing Driven
Instabilities for Advection Equations
with Application to Gauss--Lobatto
Discontinuous Galerkin Methods . . . . . 1262--1281
Brittany Froese Hamfeldt and
Tiago Salvador Higher-Order Adaptive Finite Difference
Methods for Fully Nonlinear Elliptic
Equations . . . . . . . . . . . . . . . 1282--1306
Cui-cui Ji and
Weizhong Dai and
Zhi-zhong Sun Numerical Method for Solving the
Time-Fractional Dual--Phase-Lagging Heat
Conduction Equation with the
Temperature--Jump Boundary Condition . . 1307--1336
Yixiang Luo and
Jie Xu and
Pingwen Zhang A Fast Algorithm for the Moments of
Bingham Distribution . . . . . . . . . . 1337--1350
Daisy Dahiya and
Maria Cameron Ordered Line Integral Methods for
Computing the Quasi--Potential . . . . . 1351--1384
Jianfeng Yan and
Jared Crean and
Jason E. Hicken Interior Penalties for
Summation-by-Parts Discretizations of
Linear Second-Order Differential
Equations . . . . . . . . . . . . . . . 1385--1414
Shuo Zhang and
Yingxia Xi and
Xia Ji A Multi-Level Mixed Element Method for
the Eigenvalue Problem of Biharmonic
Equation . . . . . . . . . . . . . . . . 1415--1444
Guangzhi Du and
Liyun Zuo A Parallel Partition of Unity Scheme
Based on Two--Grid Discretizations for
the Navier--Stokes Problem . . . . . . . 1445--1462
José A. Carrillo and
Bertram Düring and
Daniel Matthes and
David S. McCormick A Lagrangian Scheme for the Solution of
Nonlinear Diffusion Equations Using
Moving Simplex Meshes . . . . . . . . . 1463--1499
Sergio Amat and
Zhilin Li and
Juan Ruiz On an New Algorithm for Function
Approximation with Full Accuracy in the
Presence of Discontinuities Based on the
Immersed Interface Method . . . . . . . 1500--1534
Xiongjun Zhang and
Michael K. Ng and
Minru Bai A Fast Algorithm for Deconvolution and
Poisson Noise Removal . . . . . . . . . 1535--1554
Ali Safdari-Vaighani and
Elisabeth Larsson and
Alfa Heryudono Radial Basis Function Methods for the
Rosenau Equation and Other Higher Order
PDEs . . . . . . . . . . . . . . . . . . 1555--1580
Wuchen Li and
Penghang Yin and
Stanley Osher Computations of Optimal Transport
Distance with Fisher Information
Regularization . . . . . . . . . . . . . 1581--1595
Ernest K. Ryu and
Wuchen Li and
Penghang Yin and
Stanley Osher Unbalanced and Partial $ L_1 $
Monge--Kantorovich Problem: a Scalable
Parallel First-Order Method . . . . . . 1596--1613
A. H. Bentbib and
K. Jbilou and
Y. Kaouane A Computational Global Tangential Krylov
Subspace Method for Model Reduction of
Large--Scale MIMO Dynamical Systems . . 1614--1632
Siu-Long Lei and
Wenfei Wang and
Xu Chen and
Deng Ding A Fast Preconditioned Penalty Method for
American Options Pricing Under
Regime--Switching Tempered Fractional
Diffusion Models . . . . . . . . . . . . 1633--1655
Jingtang Ma and
Zhiqiang Zhou Convergence Analysis of Iterative
Laplace Transform Methods for the
Coupled PDEs from Regime--Switching
Option Pricing . . . . . . . . . . . . . 1656--1674
Youngsoo Ha and
Chang Ho Kim and
Hyoseon Yang and
Jungho Yoon A Sixth-Order Weighted Essentially
Non-oscillatory Schemes Based on
Exponential Polynomials for
Hamilton--Jacobi Equations . . . . . . . 1675--1700
Ricardo Delgadillo and
Xu Yang and
Jiwei Zhang Frozen Gaussian Approximation-Based
Artificial Boundary Conditions for
One-Dimensional Nonlinear Schrödinger
Equation in the Semiclassical Regime . . 1701--1720
T. S. Jang A Regular Integral Equation Formalism
for Solving the Standard Boussinesq's
Equations for Variable Water Depth . . . 1721--1756
Ali Abdi and
Jean-Paul Berrut and
Seyyed Ahmad Hosseini The Linear Barycentric Rational Method
for a Class of Delay Volterra
Integro--Differential Equations . . . . 1757--1775
Vincent Lemaire and
Mich\`ele Thieullen and
Nicolas Thomas Exact Simulation of the Jump Times of a
Class of Piecewise Deterministic Markov
Processes . . . . . . . . . . . . . . . 1776--1807
Weizheng Xu and
Weiguo Wu An Improved Third-Order WENO-Z Scheme 1808--1841
Mahkame Sharbatdar and
Carl Ollivier-Gooch Adjoint-Based Functional Correction for
Unstructured Mesh Finite Volume Methods 1--23
Adeline Kornelus and
Daniel Appelö Flux-Conservative Hermite Methods for
Simulation of Nonlinear Conservation
Laws . . . . . . . . . . . . . . . . . . 24--47
Yana Di and
Hehu Xie and
Xiaobo Yin Anisotropic Meshes and Stabilization
Parameter Design of Linear SUPG Method
for 2D Convection--Dominated
Convection--Diffusion Equations . . . . 48--68
Tianyi Lin and
Shiqian Ma and
Shuzhong Zhang Global Convergence of Unmodified
$3$-Block ADMM for a Class of Convex
Minimization Problems . . . . . . . . . 69--88
Matteo C. Aletti and
Simona Perotto and
Alessandro Veneziani HiMod Reduction of
Advection--Diffusion--Reaction Problems
with General Boundary Conditions . . . . 89--119
Guoqiao You and
Renkun Shi and
Yuhua Xu An Efficient Lagrangian Interpolation
Scheme for Computing Flow Maps and Line
Integrals using Discrete Velocity Data 120--144
B. Gross and
P. J. Atzberger Spectral Numerical Exterior Calculus
Methods for Differential Equations on
Radial Manifolds . . . . . . . . . . . . 145--165
Chuanli Wang and
Zhongqing Wang and
Lilian Wang A Spectral Collocation Method for
Nonlinear Fractional Boundary Value
Problems with a Caputo Derivative . . . 166--188
John Nicponski and
Jae-Hun Jung A Note on High--Precision Approximation
of Asymptotically Decaying Solution and
Orthogonal Decomposition . . . . . . . . 189--215
Hendrik Ranocha Comparison of Some Entropy Conservative
Numerical Fluxes for the Euler Equations 216--242
WenYi Tian and
Xiaoming Yuan Convergence Analysis of Primal--Dual
Based Methods for Total Variation
Minimization with Finite Element
Approximation . . . . . . . . . . . . . 243--274
Linia Anie Sunny and
V. Antony Vijesh A Monotone Iterative Technique for
Nonlinear Fourth Order Elliptic
Equations with Nonlocal Boundary
Conditions . . . . . . . . . . . . . . . 275--298
Robert Hannah and
Wotao Yin On Unbounded Delays in Asynchronous
Parallel Fixed--Point Algorithms . . . . 299--326
Xiang Gao and
Bo Jiang and
Shuzhong Zhang On the Information--Adaptive Variants of
the ADMM: An Iteration Complexity
Perspective . . . . . . . . . . . . . . 327--363
Xiantao Xiao and
Yongfeng Li and
Zaiwen Wen and
Liwei Zhang A Regularized Semi-Smooth Newton Method
with Projection Steps for Composite
Convex Programs . . . . . . . . . . . . 364--389
Hui Liang and
Martin Stynes Collocation Methods for General Caputo
Two--Point Boundary Value Problems . . . 390--425
David A. Kopriva Stability of Overintegration Methods for
Nodal Discontinuous Galerkin Spectral
Element Methods . . . . . . . . . . . . 426--442
Adam Reyes and
Dongwook Lee and
Carlo Graziani and
Petros Tzeferacos A New Class of High-Order Methods for
Fluid Dynamics Simulations Using
Gaussian Process Modeling:
One-Dimensional Case . . . . . . . . . . 443--480
Yifan Wang and
Annalisa Quaini and
Suncica Cani\'c A Higher-Order Discontinuous
Galerkin/Arbitrary Lagrangian Eulerian
Partitioned Approach to Solving
Fluid--Structure Interaction Problems
with Incompressible, Viscous Fluids and
Elastic Structures . . . . . . . . . . . 481--520
Carlos Lozano Entropy Production by Explicit
Runge--Kutta Schemes . . . . . . . . . . 521--564
Leijie Qiao and
Da Xu Compact Alternating Direction Implicit
Scheme for Integro--Differential
Equations of Parabolic Type . . . . . . 565--582
J. L. Gracia and
E. O'Riordan and
M. Stynes A Fitted Scheme for a Caputo
Initial--Boundary Value Problem . . . . 583--609
Jikun Zhao and
Bei Zhang and
Shaochun Chen and
Shipeng Mao The Morley--Type Virtual Element for
Plate Bending Problems . . . . . . . . . 610--629
Mikel Antoñana and
Joseba Makazaga and
Ander Murua New Integration Methods for Perturbed
ODEs Based on Symplectic Implicit
Runge--Kutta Schemes with Application to
Solar System Simulations . . . . . . . . 630--650
Lidia Aceto and
Paolo Novati Efficient Implementation of Rational
Approximations to Fractional
Differential Operators . . . . . . . . . 651--671
Long Chen and
Jun Hu and
Xuehai Huang Multigrid Methods for
Hellan--Herrmann-Johnson Mixed Method of
Kirchhoff Plate Bending Problems . . . . 673--696
Ward Melis and
Giovanni Samaey Telescopic Projective Integration for
Linear Kinetic Equations with Multiple
Relaxation Times . . . . . . . . . . . . 697--726
Gangjoon Yoon and
Chohong Min and
Seick Kim A Stable and Convergent Hodge
Decomposition Method for Fluid--Solid
Interaction . . . . . . . . . . . . . . 727--758
Jie Meng and
Sang-Hyup Seo and
Hyun-Min Kim Condition Numbers and Backward Error of
a Matrix Polynomial Equation Arising in
Stochastic Models . . . . . . . . . . . 759--776
Steven Britt and
Eli Turkel and
Semyon Tsynkov A High Order Compact Time/Space Finite
Difference Scheme for the Wave Equation
with Variable Speed of Sound . . . . . . 777--811
Gustav Ludvigsson and
Kyle R. Steffen and
Simon Sticko and
Siyang Wang and
Qing Xia and
Yekaterina Epshteyn and
Gunilla Kreiss High-Order Numerical Methods for 2D
Parabolic Problems in Single and
Composite Domains . . . . . . . . . . . 812--847
Dongfang Li and
Jiwei Zhang and
Zhimin Zhang Unconditionally Optimal Error Estimates
of a Linearized Galerkin Method for
Nonlinear Time Fractional
Reaction--Subdiffusion Equations . . . . 848--866
Minghua Chen and
Weihua Deng High Order Algorithm for the
Time-Tempered Fractional Feynman--Kac
Equation . . . . . . . . . . . . . . . . 867--887
Feifei Jing and
Weimin Han and
Wenjing Yan and
Fei Wang Discontinuous Galerkin Methods for a
Stationary Navier--Stokes Problem with a
Nonlinear Slip Boundary Condition of
Friction Type . . . . . . . . . . . . . 888--912
Huan Liu and
Aijie Cheng and
Hong Wang A Fast Discontinuous Galerkin Method for
a Bond--Based Linear Peridynamic Model
Discretized on a Locally Refined
Composite Mesh . . . . . . . . . . . . . 913--942
Giovanna Califano and
Giuseppe Izzo and
Zdzislaw Jackiewicz Strong Stability Preserving General
Linear Methods with Runge--Kutta
Stability . . . . . . . . . . . . . . . 943--968
Svenja Schoeder and
Martin Kronbichler and
Wolfgang A. Wall Arbitrary High-Order Explicit
Hybridizable Discontinuous Galerkin
Methods for the Acoustic Wave Equation 969--1006
Yuan-Ming Wang and
Lei Ren High-Order Compact Difference Methods
for Caputo--Type Variable Coefficient
Fractional Sub-diffusion Equations in
Conservative Form . . . . . . . . . . . 1007--1043
Issei Oikawa An HDG Method with Orthogonal
Projections in Facet Integrals . . . . . 1044--1054
Fujun Cao and
Zhiqiang Sheng and
Guangwei Yuan Monotone Finite Volume Schemes for
Diffusion Equation with Imperfect
Interface on Distorted Meshes . . . . . 1055--1077
Weina Wang and
Chunlin Wu and
Jiansong Deng A General Selective Averaging Method for
Piecewise Constant Signal and Image
Processing . . . . . . . . . . . . . . . 1078--1104
Xinghui Zhong and
Qin Li Galerkin Methods for Stationary
Radiative Transfer Equations with
Uncertain Coefficients . . . . . . . . . 1105--1126
Xinjuan Chen and
Jae-Hun Jung and
Anne Gelb Finite Fourier Frame Approximation Using
the Inverse Polynomial Reconstruction
Method . . . . . . . . . . . . . . . . . 1127--1147
Ruihan Guo and
Francis Filbet A $p$-Adaptive Local Discontinuous
Galerkin Level Set Method for Willmore
Flow . . . . . . . . . . . . . . . . . . 1148--1167
Zhengjie Sun and
Zongmin Wu Meshless Conservative Scheme for
Multivariate Nonlinear Hamiltonian PDEs 1168--1187
Yufang Huang and
Jianfeng Lu and
Pingbing Ming A Concurrent Global--Local Numerical
Method for Multiscale PDEs . . . . . . . 1188--1215
Ming-Cheng Shiue and
Kian Chuan Ong and
Ming-Chih Lai Convergence of the MAC Scheme for the
Stokes/Darcy Coupling Problem . . . . . 1216--1251
Seakweng Vong and
Pin Lyu Unconditional Convergence in
Maximum--Norm of a Second-Order
Linearized Scheme for a Time-Fractional
Burgers--Type Equation . . . . . . . . . 1252--1273
Gang Wang and
Yinnian He and
Jinjin Yang Weak Galerkin Finite Element Methods for
the Simulation of Single--Phase Flow in
Fractured Porous Media . . . . . . . . . 1274--1300
Zhan Ma and
Song-Ping Wu HWENO Schemes Based on Compact
Differencefor Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 1301--1325
Jan Nordström and
Hannes Frenander On Long Time Error Bounds for the Wave
Equation on Second Order Form . . . . . 1327--1336
Inmaculada Higueras and
David I. Ketcheson and
Tihamér A. Kocsis Optimal Monotonicity--Preserving
Perturbations of a Given Runge--Kutta
Method . . . . . . . . . . . . . . . . . 1337--1369
David P. Nicholls and
Xin Tong High-Order Perturbation of Surfaces
Algorithms for the Simulation of
Localized Surface Plasmon Resonances in
Two Dimensions . . . . . . . . . . . . . 1370--1395
Penghang Yin and
Jack Xin and
Yingyong Qi Linear Feature Transform and Enhancement
of Classification on Deep Neural Network 1396--1406
Guoqiao You and
Shingyu Leung An Improved Eulerian Approach for the
Finite Time Lyapunov Exponent . . . . . 1407--1435
Weiwei Hu and
Jiguang Shen and
John R. Singler and
Yangwen Zhang and
Xiaobo Zheng A Superconvergent HDG Method for
Distributed Control of Convection
Diffusion PDEs . . . . . . . . . . . . . 1436--1457
Yao Rong and
William Layton and
Haiyun Zhao Numerical Analysis of an Artificial
Compression Method for
Magnetohydrodynamic Flows at Low
Magnetic Reynolds Numbers . . . . . . . 1458--1483
Sander Rhebergen and
Garth N. Wells A Hybridizable Discontinuous Galerkin
Method for the Navier--Stokes Equations
with Pointwise Divergence--Free Velocity
Field . . . . . . . . . . . . . . . . . 1484--1501
Xuehua Yang and
Haixiang Zhang and
Da Xu WSGD-OSC Scheme for Two-Dimensional
Distributed Order Fractional
Reaction--Diffusion Equation . . . . . . 1502--1520
Vishal Singh and
Hossain Chizari and
Farzad Ismail Non-unified Compact
Residual--Distribution Methods for
Scalar Advection--Diffusion Problems . . 1521--1546
Jie Du and
Eric T. Chung and
Ming Fai Lam and
Xiao-Ping Wang Discontinuous Galerkin Method with
Staggered Hybridization for a Class of
Nonlinear Stokes Equations . . . . . . . 1547--1577
John C. Bowman and
Zayd Ghoggali The Partial Fast Fourier Transform . . . 1578--1593
Ying Jiang and
Bo Wang and
Yuesheng Xu A Fully Discrete Fast Fourier--Galerkin
Method Solving a Boundary Integral
Equation for the Biharmonic Equation . . 1594--1632
Jin Zhang and
Xiaowei Liu Supercloseness of Continuous Interior
Penalty Methods on Shishkin Triangular
Meshes and Hybrid Meshes for Singularly
Perturbed Problems with Characteristic
Layers . . . . . . . . . . . . . . . . . 1633--1656
Masaru Miyashita and
Norikazu Saito Hybridized Discontinuous Galerkin Method
for Elliptic Interface Problems: Error
Estimates Under Low Regularity
Assumptions of Solutions . . . . . . . . 1657--1673
T. Askham A Stabilized Separation of Variables
Method for the Modified Biharmonic
Equation . . . . . . . . . . . . . . . . 1674--1697
Ming Yan A New Primal--Dual Algorithm for
Minimizing the Sum of Three Functions
with a Linear Operator . . . . . . . . . 1698--1717
Hongjin He and
Chen Ling and
Liqun Qi and
Guanglu Zhou A Globally and Quadratically Convergent
Algorithm for Solving Multilinear
Systems with $ {{\mathcal {M}}}$-tensors 1718--1741
Jeremy E. Kozdon and
Lucas C. Wilcox An Energy Stable Approach for
Discretizing Hyperbolic Equations with
Nonconforming Discontinuous Galerkin
Methods . . . . . . . . . . . . . . . . 1742--1784
Renzhong Feng and
Junna Duan High Accurate Finite Differences Based
on RBF Interpolation and its Application
in Solving Differential Equations . . . 1785--1812
Weiqi Zhou and
Haijun Wu An Adaptive Finite Element Method for
the Diffraction Grating Problem with PML
and Few--Mode DtN Truncations . . . . . 1813--1838
Yangang Chen and
Justin W. L. Wan and
Jessey Lin Monotone Mixed Finite Difference Scheme
for Monge--Amp\`ere Equation . . . . . . 1839--1867
Mahboub Baccouch Asymptotically Exact Posteriori Error
Estimates for the Local Discontinuous
Galerkin Method Applied to Nonlinear
Convection--Diffusion Problems . . . . . 1868--1904
Weijia Li and
Wenbin Chen and
Cheng Wang and
Yue Yan and
Ruijian He A Second Order Energy Stable Linear
Scheme for a Thin Film Model Without
Slope Selection . . . . . . . . . . . . 1905--1937
Wenqiang Feng and
Zhen Guan and
John Lowengrub and
Cheng Wang and
Steven M. Wise and
Ying Chen A Uniquely Solvable, Energy Stable
Numerical Scheme for the Functionalized
Cahn--Hilliard Equation and Its
Convergence Analysis . . . . . . . . . . 1938--1967
Jorge E. Macías-Díaz A Numerically Efficient
Dissipation--Preserving Implicit Method
for a Nonlinear Multidimensional
Fractional Wave Equation . . . . . . . . 1--26
Wenping Fan and
Xiaoyun Jiang and
Fawang Liu and
Vo Anh The Unstructured Mesh Finite Element
Method for the Two-Dimensional
Multi-term Time--Space Fractional
Diffusion--Wave Equation on an Irregular
Convex Domain . . . . . . . . . . . . . 27--52
Alexandre Caboussat and
Roland Glowinski and
Dimitrios Gourzoulidis A Least-Squares/Relaxation Method for
the Numerical Solution of the
Three-Dimensional Elliptic
Monge--Amp\`ere Equation . . . . . . . . 53--78
Yongxin Chen and
Eldad Haber and
Kaoru Yamamoto and
Tryphon T. Georgiou and
Allen Tannenbaum An Efficient Algorithm for Matrix-Valued
and Vector-Valued Optimal Mass Transport 79--100
Long Chen and
Yongke Wu and
Lin Zhong and
Jie Zhou MultiGrid Preconditioners for Mixed
Finite Element Methods of the Vector
Laplacian . . . . . . . . . . . . . . . 101--128
Roberto Garrappa and
Marina Popolizio Computing the Matrix Mittag-Leffler
Function with Applications to Fractional
Calculus . . . . . . . . . . . . . . . . 129--153
Gregor J. Gassner and
Andrew R. Winters and
Florian J. Hindenlang and
David A. Kopriva The BR1 Scheme is Stable for the
Compressible Navier--Stokes Equations 154--200
Gregor J. Gassner and
Andrew R. Winters and
Florian J. Hindenlang and
David A. Kopriva Correction to: The BR1 Scheme is Stable
for the Compressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 201--203
Harbir Antil and
Enrique Otárola and
Abner J. Salgado Optimization with Respect to Order in a
Fractional Diffusion Model: Analysis,
Approximation and Algorithmic Aspects 204--224
Han Zhou and
Paul Andries Zegeling Stability and Convergence Analysis of a
Class of Continuous Piecewise Polynomial
Approximations for Time-Fractional
Differential Equations . . . . . . . . . 225--262
Tao Xiong and
Giovanni Russo and
Jing-Mei Qiu High Order Multi-dimensional
Characteristics Tracing for the
Incompressible Euler Equation and the
Guiding--Center Vlasov Equation . . . . 263--282
Fanhai Zeng and
Ian Turner and
Kevin Burrage A Stable Fast Time-Stepping Method for
Fractional Integral and Derivative
Operators . . . . . . . . . . . . . . . 283--307
Juan Pablo Borthagaray and
Leandro M. Del Pezzo and
Sandra Martínez Finite Element Approximation for the
Fractional Eigenvalue Problem . . . . . 308--329
Vrushali A. Bokil and
Yingda Cheng and
Yan Jiang and
Fengyan Li and
Puttha Sakkaplangkul High Spatial Order Energy Stable FDTD
Methods for Maxwell's Equations in
Nonlinear Optical Media in One Dimension 330--371
S. Geevers and
W. A. Mulder and
J. J. W. van der Vegt Dispersion Properties of Explicit Finite
Element Methods for Wave Propagation
Modelling on Tetrahedral Meshes . . . . 372--396
Vidhi Zala and
Varun Shankar and
Shankar P. Sastry and
Robert M. Kirby Curvilinear Mesh Adaptation Using Radial
Basis Function Interpolation and
Smoothing . . . . . . . . . . . . . . . 397--418
Gang Bao and
Yanzhao Cao and
Yongle Hao and
Kai Zhang A Robust Numerical Method for the Random
Interface Grating Problem via Shape
Calculus, Weak Galerkin Method, and
Low-Rank Approximation . . . . . . . . . 419--442
Mark Ainsworth and
Guosheng Fu Fully Computable a Posteriori Error
Bounds for Hybridizable Discontinuous
Galerkin Finite Element Approximations 443--466
Hailiang Liu and
Peimeng Yin A Mixed Discontinuous Galerkin Method
Without Interior Penalty for
Time-Dependent Fourth Order Problems . . 467--501
Hee Jun Yang and
Hyea Hyun Kim A Hybrid Staggered Discontinuous
Galerkin Method for KdV Equations . . . 502--523
Liang Ge and
Lianhai Wang and
Yanzhen Chang A Sparse Grid Stochastic Collocation
Upwind Finite Volume Element Method for
the Constrained Optimal Control Problem
Governed by Random Convection Diffusion
Equations . . . . . . . . . . . . . . . 524--551
Jie Wu and
Yuan-yuan He and
Guo-hao Ding and
Yi-yu Han Hybrid Optimized Low-Dissipation and
Adaptive MUSCL Reconstruction Technique
for Hyperbolic Conservation Laws . . . . 552--578
B. W. Wissink and
G. B. Jacobs and
J. K. Ryan and
W. S. Don and
E. T. A. van der Weide Shock Regularization with
Smoothness--Increasing
Accuracy--Conserving Dirac--Delta
Polynomial Kernels . . . . . . . . . . . 579--596
Tingwei Meng and
Lok Ming Lui PCBC: Quasiconformality of Point Cloud
Mappings . . . . . . . . . . . . . . . . 597--633
Georgios E. Zouraris A Linear Implicit Finite Difference
Discretization of the Schrödinger--Hirota
Equation . . . . . . . . . . . . . . . . 634--656
Suna Ma and
Huiyuan Li and
Zhimin Zhang Efficient Spectral Methods for Some
Singular Eigenvalue Problems . . . . . . 657--688
Lucas Friedrich and
Andrew R. Winters and
David C. Del Rey Fernández and
Gregor J. Gassner and
Matteo Parsani and
Mark H. Carpenter An Entropy Stable $ h / p $
Non-Conforming Discontinuous Galerkin
Method with the Summation-by-Parts
Property . . . . . . . . . . . . . . . . 689--725
Haitao Dong and
Fujun Liu Numerical Methods for Euler Equations
with Self-similar and Quasi Self-similar
Solutions . . . . . . . . . . . . . . . 726--754
Oskar Ålund and
Jan Nordström A Stable Domain Decomposition Technique
for Advection--Diffusion Problems . . . 755--774
Siyang Wang An Improved High Order Finite Difference
Method for Non-conforming Grid
Interfaces for the Wave Equation . . . . 775--792
Huadong Gao and
Pengtao Sun A Linearized Local Conservative Mixed
Finite Element Method for
Poisson--Nernst--Planck Equations . . . 793--817
Huadong Gao and
Pengtao Sun Correction to: A Linearized Local
Conservative Mixed Finite Element Method
for Poisson--Nernst--Planck Equations 818--818
Debojyoti Ghosh and
Mikhail A. Dorf and
Milo R. Dorr and
Jeffrey A. F. Hittinger Kinetic Simulation of Collisional
Magnetized Plasmas with Semi-implicit
Time Integration . . . . . . . . . . . . 819--849
S. Boscarino and
G. Russo and
L. Scandurra All Mach Number Second Order
Semi-implicit Scheme for the Euler
Equations of Gas Dynamics . . . . . . . 850--884
Alessio Fumagalli and
Isabelle Faille A Double--Layer Reduced Model for Fault
Flow on Slipping Domains with an Hybrid
Finite Volume Scheme . . . . . . . . . . 885--910
Myeongmin Kang and
Myungjoo Kang and
Miyoun Jung Image Colorization Based on a
Generalization of the Low Dimensional
Manifold Model . . . . . . . . . . . . . 911--935
Chris Finlay and
Adam M. Oberman Approximate Homogenization of Fully
Nonlinear Elliptic PDEs: Estimates and
Numerical Results for Pucci Type
Equations . . . . . . . . . . . . . . . 936--949
Daniele Bertaccini and
Fabio Durastante Limited Memory Block Preconditioners for
Fast Solution of Fractional Partial
Differential Equations . . . . . . . . . 950--970
Massimo Frittelli and
Anotida Madzvamuse and
Ivonne Sgura and
Chandrasekhar Venkataraman Numerical Preservation of Velocity
Induced Invariant Regions for
Reaction--Diffusion Systems on Evolving
Surfaces . . . . . . . . . . . . . . . . 971--1000
Lingling Zhou and
Yan Xu Stability Analysis and Error Estimates
of Semi-implicit Spectral Deferred
Correction Coupled with Local
Discontinuous Galerkin Method for Linear
Convection--Diffusion Equations . . . . 1001--1029
Adam J. Crowder and
Catherine E. Powell CBS Constants & Their Role in Error
Estimation for Stochastic Galerkin
Finite Element Methods . . . . . . . . . 1030--1054
Philippe Bocher and
Juan I. Montijano and
Luis Rández and
Marnix Van Daele Explicit Runge--Kutta Methods for Stiff
Problems with a Gap in Their Eigenvalue
Spectrum . . . . . . . . . . . . . . . . 1055--1083
Chieh-Sen Huang and
Todd Arbogast An Implicit Eulerian--Lagrangian WENO3
Scheme for Nonlinear Conservation Laws 1084--1114
Diego Álvarez and
Pedro González-Rodríguez and
Miguel Moscoso A Closed--Form Formula for the
RBF--Based Approximation of the
Laplace--Beltrami Operator . . . . . . . 1115--1132
Penghang Yin and
Minh Pham and
Adam Oberman and
Stanley Osher Stochastic Backward Euler: an Implicit
Gradient Descent Algorithm for $k$-Means
Clustering . . . . . . . . . . . . . . . 1133--1146
Yibao Li and
Xuelin Qi and
Junseok Kim Direct Discretization Method for the
Cahn--Hilliard Equation on an Evolving
Surface . . . . . . . . . . . . . . . . 1147--1163
Binjie Li and
Hao Luo and
Xiaoping Xie A Time-Spectral Algorithm for Fractional
Wave Problems . . . . . . . . . . . . . 1164--1184
Lin Wang and
Haijun Yu On Efficient Second Order Stabilized
Semi-implicit Schemes for the
Cahn--Hilliard Phase--Field Equation . . 1185--1209
Daozhi Han and
Xiaoming Wang A Second Order in Time, Decoupled,
Unconditionally Stable Numerical Scheme
for the Cahn--Hilliard-Darcy System . . 1210--1233
Susanne C. Brenner and
Amanda E. Diegel and
Li-Yeng Sung A Robust Solver for a Mixed Finite
Element Method for the Cahn--Hilliard
Equation . . . . . . . . . . . . . . . . 1234--1249
Shu-sheng Chen and
Chao Yan and
Bo-xi Lin and
Yan-su Li A New Robust Carbuncle--Free Roe Scheme
for Strong Shock . . . . . . . . . . . . 1250--1277
Ylva Rydin and
Ken Mattsson and
Jonatan Werpers High-fidelity Sound Propagation in a
Varying 3D Atmosphere . . . . . . . . . 1278--1302
Yanlai Chen and
Bo Dong and
Chi-Wang Shu A Foreword to the Special Issue in Honor
of Professor Bernardo Cockburn on His
60th Birthday: a Life Time of
Discontinuous Schemings . . . . . . . . 1303--1309
Joubine Aghili and
Daniele A. Di Pietro An Advection-Robust Hybrid High-Order
Method for the Oseen Problem . . . . . . 1310--1338
Paola F. Antonietti and
Paul Houston and
Giorgio Pennesi Fast Numerical Integration on Polytopic
Meshes with Applications to
Discontinuous Galerkin Finite Element
Methods . . . . . . . . . . . . . . . . 1339--1370
Jerry L. Bona and
Hongqiu Chen and
Ohannes Karakashian and
Michael M. Wise Finite Element Methods for a System of
Dispersive Equations . . . . . . . . . . 1371--1401
Waixiang Cao and
Zhimin Zhang Some Recent Developments in
Superconvergence of Discontinuous
Galerkin Methods for Time-Dependent
Partial Differential Equations . . . . . 1402--1423
Karol L. Cascavita and
Jérémy Bleyer and
Xavier Chateau and
Alexandre Ern Hybrid Discretization Methods with
Adaptive Yield Surface Detection for
Bingham Pipe Flows . . . . . . . . . . . 1424--1443
P. Castillo and
S. Gómez On the Conservation of Fractional
Nonlinear Schrödinger Equation's
Invariants by the Local Discontinuous
Galerkin Method . . . . . . . . . . . . 1444--1467
Sheng Chen and
Jie Shen Enriched Spectral Methods and
Applications to Problems with Weakly
Singular Solutions . . . . . . . . . . . 1468--1489
Jie Du and
Eric Chung An Adaptive Staggered Discontinuous
Galerkin Method for the Steady State
Convection--Diffusion Equation . . . . . 1490--1518
Aseel Farhat and
Hans Johnston and
Michael Jolly and
Edriss S. Titi Assimilation of Nearly Turbulent
Rayleigh--Bénard Flow Through Vorticity
or Local Circulation Measurements: a
Computational Study . . . . . . . . . . 1519--1533
Xiaobing Feng and
Thomas Lewis Nonstandard Local Discontinuous Galerkin
Methods for Fully Nonlinear Second Order
Elliptic and Parabolic Equations in High
Dimensions . . . . . . . . . . . . . . . 1534--1565
P. Fernandez and
A. Christophe and
S. Terrana and
N. C. Nguyen and
J. Peraire Hybridized Discontinuous Galerkin
Methods for Wave Propagation . . . . . . 1566--1604
Guosheng Fu and
Christoph Lehrenfeld A Strongly Conservative Hybrid DG/Mixed
FEM for the Coupling of Stokes and Darcy
Flow . . . . . . . . . . . . . . . . . . 1605--1620
Pei Fu and
Fengyan Li and
Yan Xu Globally Divergence--Free Discontinuous
Galerkin Methods for Ideal
Magnetohydrodynamic Equations . . . . . 1621--1659
Huadong Gao and
Weifeng Qiu Error Analysis of Mixed Finite Element
Methods for Nonlinear Parabolic
Equations . . . . . . . . . . . . . . . 1660--1678
Matteo Giacomini and
Alexandros Karkoulias and
Ruben Sevilla and
Antonio Huerta A Superconvergent HDG Method for Stokes
Flow with Strongly Enforced Symmetry of
the Stress Tensor . . . . . . . . . . . 1679--1702
Jay Gopalakrishnan and
Manuel Solano and
Felipe Vargas Dispersion Analysis of HDG Methods . . . 1703--1735
Johnny Guzman and
Alexandre Madureira and
Marcus Sarkis and
Shawn Walker Analysis of the Finite Element Method
for the Laplace--Beltrami Equation on
Surfaces with Regions of High Curvature
Using Graded Meshes . . . . . . . . . . 1736--1761
Guido Kanschat and
Beatrice Riviere A Finite Element Method with Strong Mass
Conservation for Biot's Linear
Consolidation Model . . . . . . . . . . 1762--1779
Guanglian Li and
Ke Shi Upscaled HDG Methods for Brinkman
Equations with High--Contrast
Heterogeneous Coefficient . . . . . . . 1780--1800
Dan Ling and
Juan Cheng and
Chi-Wang Shu Conservative High Order
Positivity--Preserving Discontinuous
Galerkin Methods for Linear Hyperbolic
and Radiative Transfer Equations . . . . 1801--1831
Jorge Albella Martínez and
Sébastien Imperiale and
Patrick Joly and
Jerónimo Rodríguez Solving $2$D Linear Isotropic
Elastodynamics by Means of Scalar
Potentials: a New Challenge for Finite
Elements . . . . . . . . . . . . . . . . 1832--1873
Lorenzo Mascotto and
Ilaria Perugia and
Alexander Pichler Non-conforming Harmonic Virtual Element
Method: $h$- and $p$-Versions . . . . . 1874--1908
Fabian Müller and
Dominik Schötzau and
Christoph Schwab Discontinuous Galerkin Methods for
Acoustic Wave Propagation in Polygons 1909--1935
Sander Rhebergen and
Garth N. Wells Preconditioning of a Hybridized
Discontinuous Galerkin Finite Element
Method for the Stokes Equations . . . . 1936--1952
Ruben Sevilla and
Antonio Huerta HDG-NEFEM with Degree Adaptivity for
Stokes Flows . . . . . . . . . . . . . . 1953--1980
Haijin Wang and
Jingjing Zheng and
Fan Yu and
Hui Guo and
Qiang Zhang Local Discontinuous Galerkin Method with
Implicit--Explicit Time Marching for
Incompressible Miscible Displacement
Problem in Porous Media . . . . . . . . 1--28
Yu Wang and
Wotao Yin and
Jinshan Zeng Global Convergence of ADMM in Nonconvex
Nonsmooth Optimization . . . . . . . . . 29--63
S. Kumar and
R. Ruiz-Baier and
R. Sandilya Error Bounds for Discontinuous Finite
Volume Discretisations of Brinkman
Optimal Control Problems . . . . . . . . 64--93
Anne Gelb and
Theresa Scarnati Reducing Effects of Bad Data Using
Variance Based Joint Sparsity Recovery 94--120
Weimin Han and
Limin He and
Fei Wang Optimal Order Error Estimates for
Discontinuous Galerkin Methods for the
Wave Equation . . . . . . . . . . . . . 121--144
Min Li and
Hicham Chaouki and
Jean-Loup Robert and
Donald Ziegler and
Mario Fafard Numerical Simulation of Stefan Problem
Coupled with Mass Transport in a Binary
System Through XFEM/Level Set Method . . 145--166
Mahesh Narayanamurthi and
Paul Tranquilli and
Adrian Sandu and
Mayya Tokman EPIRK-W and EPIRK-K Time Discretization
Methods . . . . . . . . . . . . . . . . 167--201
Zhaoxiang Li and
Bingbing Ji and
Jianxin Zhou A Local Minimax Method Using Virtual
Geometric Objects: Part I --- For
Finding Saddles . . . . . . . . . . . . 202--225
Zhaoxiang Li and
Jianxin Zhou A Local Minimax Method Using Virtual
Geometric Objects: Part II --- For
Finding Equality Constrained Saddles . . 226--245
Pitágoras P. Carvalho and
Enrique Fernández-Cara On the Computation of Nash and Pareto
Equilibria for Some Bi-objective Control
Problems . . . . . . . . . . . . . . . . 246--273
Shun Zhang and
Erich Novak Optimal Quadrature Formulas for the
Sobolev Space $ H^1 $ . . . . . . . . . 274--289
Jianguo Huang and
Xuehai Huang A Hybridizable Discontinuous Galerkin
Method for Kirchhoff Plates . . . . . . 290--320
Mahendra Paipuri and
Carlos Tiago and
Sonia Fernández-Méndez Coupling of Continuous and Hybridizable
Discontinuous Galerkin Methods:
Application to Conjugate Heat Transfer
Problem . . . . . . . . . . . . . . . . 321--350
Hai Bi and
Jiayu Han and
Yidu Yang Local and Parallel Finite Element
Algorithms for the Transmission
Eigenvalue Problem . . . . . . . . . . . 351--375
H. Herrero and
F. Pla and
M. Ruiz-Ferrández A Schwarz Method for a Rayleigh--Bénard
Problem . . . . . . . . . . . . . . . . 376--392
Giacomo Dimarco and
Cory Hauck and
Raphaël Loub\`ere A Class of Low Dissipative Schemes for
Solving Kinetic Equations . . . . . . . 393--432
Andrés M. Rueda-Ramírez and
Gonzalo Rubio and
Esteban Ferrer and
Eusebio Valero Truncation Error Estimation in the
$p$-Anisotropic Discontinuous Galerkin
Spectral Element Method . . . . . . . . 433--466
Hong Sun and
Xuan Zhao and
Zhi-zhong Sun The Temporal Second Order Difference
Schemes Based on the Interpolation
Approximation for the Time Multi-term
Fractional Wave Equation . . . . . . . . 467--498
Antonio Baeza and
Raimund Bürger and
Pep Mulet and
David Zorío Central WENO Schemes Through a Global
Average Weight . . . . . . . . . . . . . 499--530
Jinyan Fan and
Jianchao Huang and
Jianyu Pan An Adaptive Multi-step
Levenberg--Marquardt Method . . . . . . 531--548
Min Li and
Chengming Huang The Linear Barycentric Rational
Quadrature Method for Auto--Convolution
Volterra Integral Equations . . . . . . 549--564
Chris D. Cantwell and
Allan S. Nielsen A Minimally Intrusive Low-Memory
Approach to Resilience for Existing
Transient Solvers . . . . . . . . . . . 565--581
Mohamed M. S. Nasser Numerical Computing of Preimage Domains
for Bounded Multiply Connected Slit
Domains . . . . . . . . . . . . . . . . 582--606
Jun Liu and
Stanley Osher Block Matching Local SVD Operator Based
Sparsity and TV Regularization for Image
Denoising . . . . . . . . . . . . . . . 607--624
P. F. Antonietti and
G. Pennesi V-cycle Multigrid Algorithms for
Discontinuous Galerkin Methods on
Non-nested Polytopic Meshes . . . . . . 625--652
Chaoxu Pei and
Mark Sussman and
M. Yousuff Hussaini New Multi-implicit Space--Time Spectral
Element Methods for
Advection--Diffusion-Reaction Problems 653--686
Suxiang Yang and
Huanzhen Chen and
Hong Wang Least-Squared Mixed Variational
Formulation Based on Space Decomposition
for a Kind of Variable--Coefficient
Fractional Diffusion Problems . . . . . 687--709
Daan Huybrechs and
Peter Opsomer High-Frequency Asymptotic Compression of
Dense BEM Matrices for General
Geometries Without Ray Tracing . . . . . 710--745
Dong-Lin Sun and
Ting-Zhu Huang and
Bruno Carpentieri and
Yan-Fei Jing A New Shifted Block GMRES Method with
Inexact Breakdowns for Solving
Multi-Shifted and Multiple Right--Hand
Sides Linear Systems . . . . . . . . . . 746--769
Dong-Lin Sun and
Ting-Zhu Huang and
Bruno Carpentieri and
Yan-Fei Jing Correction to: A New Shifted Block GMRES
Method with Inexact Breakdowns for
Solving Multi-Shifted and Multiple
Right-Hand Sides Linear Systems . . . . 770--771
Anqi Chen and
Fengyan Li and
Yingda Cheng An Ultra-weak Discontinuous Galerkin
Method for Schrödinger Equation in One
Dimension . . . . . . . . . . . . . . . 772--815
Pei Fu and
Yingda Cheng and
Fengyan Li and
Yan Xu Discontinuous Galerkin Methods with
Optimal $ L^2 $ Accuracy for One
Dimensional Linear PDEs with High Order
Spatial Derivatives . . . . . . . . . . 816--863
Long Chen and
Feng Wang A Divergence Free Weak Virtual Element
Method for the Stokes Problem on
Polytopal Meshes . . . . . . . . . . . . 864--886
Javier A. Almonacid and
Gabriel N. Gatica and
Ricardo Oyarzúa A Posteriori Error Analysis of a
Mixed--Primal Finite Element Method for
the Boussinesq Problem with
Temperature--Dependent Viscosity . . . . 887--917
M. Paul Laiu and
Cory D. Hauck Positivity Limiters for Filtered
Spectral Approximations of Linear
Kinetic Transport Equations . . . . . . 918--950
Chang-Ock Lee and
Changmin Nam and
Jongho Park Domain Decomposition Methods Using Dual
Conversion for the Total Variation
Minimization with $ L^1 $ Fidelity Term 951--970
Ayoub Gouasmi and
Scott M. Murman and
Karthik Duraisamy Entropy Conservative Schemes and the
Receding Flow Problem . . . . . . . . . 971--994
Philipp Birken and
Jonathan Bull and
Antony Jameson Preconditioned Smoothers for the Full
Approximation Scheme for the RANS
Equations . . . . . . . . . . . . . . . 995--1022
Guoyi Ke and
Wei Guo An Alternative Formulation of
Discontinous Galerkin Schemes for
Solving Hamilton--Jacobi Equations . . . 1023--1044
David Moxey and
Shankar P. Sastry and
Robert M. Kirby Interpolation Error Bounds for
Curvilinear Finite Elements and Their
Implications on Adaptive Mesh Refinement 1045--1062
Juntao You and
Yuling Jiao and
Xiliang Lu and
Tieyong Zeng A Nonconvex Model with Minimax Concave
Penalty for Image Restoration . . . . . 1063--1086
Zhongqiang Zhang Error Estimates of Spectral Galerkin
Methods for a Linear Fractional
Reaction--Diffusion Equation . . . . . . 1087--1110
Masato Kimura and
Hirofumi Notsu and
Yoshimi Tanaka and
Hiroki Yamamoto The Gradient Flow Structure of an
Extended Maxwell Viscoelastic Model and
a Structure--Preserving Finite Element
Scheme . . . . . . . . . . . . . . . . . 1111--1131
Eric M. Wolf and
Christopher R. Schrock Adaptive Modal Filters Based on
Artificial and Spectral Viscosity
Techniques . . . . . . . . . . . . . . . 1132--1151
Ketan Mittal and
Paul Fischer Mesh Smoothing for the Spectral Element
Method . . . . . . . . . . . . . . . . . 1152--1173
Peter Zaspel Algorithmic Patterns for $ \mathcal
{H}$-Matrices on Many--Core Processors 1174--1206
Lixiu Wang and
Qian Zhang and
Zhimin Zhang Superconvergence Analysis and PPR
Recovery of Arbitrary Order Edge
Elements for Maxwell's Equations . . . . 1207--1230
Seyyed Abbas Mohammadi and
Farid Bozorgnia and
Heinrich Voss Optimal Shape Design for the
$p$-Laplacian Eigenvalue Problem . . . . 1231--1249
Daniele Boffi and
Lucia Gastaldi and
Rodolfo Rodríguez and
Ivana \vSebestová A Posteriori Error Estimates for
Maxwell's Eigenvalue Problem . . . . . . 1250--1271
Helmut Harbrecht and
Peter Zaspel On the Algebraic Construction of Sparse
Multilevel Approximations of Elliptic
Tensor Product Problems . . . . . . . . 1272--1290
U. S. Vevek and
B. Zang and
T. H. New On Alternative Setups of the Double Mach
Reflection Problem . . . . . . . . . . . 1291--1303
Jia Li and
Dazhi Zhang and
Xiong Meng and
Boying Wu Analysis of Discontinuous Galerkin
Methods with Upwind-Biased Fluxes for
One Dimensional Linear Hyperbolic
Equations with Degenerate Variable
Coefficients . . . . . . . . . . . . . . 1305--1328
Liyuan Chen and
Yutian Li and
Tieyong Zeng Variational Image Restoration and
Segmentation with Rician Noise . . . . . 1329--1352
Mei-Heng Yueh and
Wen-Wei Lin and
Chin-Tien Wu and
Shing-Tung Yau A Novel Stretch Energy Minimization
Algorithm for Equiareal
Parameterizations . . . . . . . . . . . 1353--1386
Li Guo and
Xingjie Helen Li and
Yang Yang Energy Dissipative Local Discontinuous
Galerkin Methods for Keller--Segel
Chemotaxis Model . . . . . . . . . . . . 1387--1404
Jérôme Droniou and
Bishnu P. Lamichhane and
Devika Shylaja The Hessian Discretisation Method for
Fourth Order Linear Elliptic Equations 1405--1437
Qiang Du and
Lili Ju and
Jianfang Lu Analysis of Fully Discrete
Approximations for Dissipative Systems
and Application to Time-Dependent
Nonlocal Diffusion Problems . . . . . . 1438--1466
Qing Cheng and
Jie Shen and
Xiaofeng Yang Highly Efficient and Accurate Numerical
Schemes for the Epitaxial Thin Film
Growth Models by Using the SAV Approach 1467--1487
Chun Pong Lau and
Yu Hin Lai and
Lok Ming Lui Variational Models for Joint Subsampling
and Reconstruction of
Turbulence-Degraded Images . . . . . . . 1488--1525
Alessandro Buccini and
Lothar Reichel An $ \ell^2$--$ \ell^q$ Regularization
Method for Large Discrete Ill-Posed
Problems . . . . . . . . . . . . . . . . 1526--1549
Luc Pronzato and
Anatoly Zhigljavsky Measures Minimizing Regularized
Dispersion . . . . . . . . . . . . . . . 1550--1570
Wanfang Shen and
Liang Ge and
Wenbin Liu Stochastic Galerkin Method for Optimal
Control Problem Governed by Random
Elliptic PDE with State Constraints . . 1571--1600
Yuval Harness Low-Dimensional Spatial Embedding Method
for Shape Uncertainty Quantification in
Acoustic Scattering by 2D Star Shaped
Obstacles . . . . . . . . . . . . . . . 1601--1631
Yaning Xie and
Wenjun Ying A Fourth-Order Kernel-Free Boundary
Integral Method for the Modified
Helmholtz Equation . . . . . . . . . . . 1632--1658
Yaning Xie and
Wenjun Ying Correction to: a Fourth-Order
Kernel-Free Boundary Integral Method for
the Modified Helmholtz Equation . . . . 1659--1659
Di Zhao and
Qiang Zhang Local Discontinuous Galerkin Methods
with Generalized Alternating Numerical
Fluxes for Two-dimensional Linear
Sobolev Equation . . . . . . . . . . . . 1660--1690
Joost Berkhout and
Bernd F. Heidergott The Jump Start Power Method: a New
Approach for Computing the Ergodic
Projector of a Finite Markov Chain . . . 1691--1723
Hongfei Fu and
Hong Wang A Preconditioned Fast Parareal Finite
Difference Method for Space--Time
Fractional Partial Differential Equation 1724--1743
Yunyun Ma and
Yuesheng Xu Computing Integrals Involved the
Gaussian Function with a Small Standard
Deviation . . . . . . . . . . . . . . . 1744--1767
Somayyeh Sheikholeslami and
James V. Lambers and
Carley Walker Convergence Analysis of Krylov Subspace
Spectral Methods for Reaction--Diffusion
Equations . . . . . . . . . . . . . . . 1768--1789
Ximei Yang and
Yanqin Bai An Adaptive Infeasible--Interior-Point
Method with the One-Norm Wide
Neighborhood for Semi-definite
Programming . . . . . . . . . . . . . . 1790--1810
Roland Glowinski and
Hao Liu and
Shingyu Leung and
Jianliang Qian A Finite Element/Operator-Splitting
Method for the Numerical Solution of the
Two Dimensional Elliptic Monge--Amp\`ere
Equation . . . . . . . . . . . . . . . . 1--47
Roland Glowinski and
Hao Liu and
Shingyu Leung and
Jianliang Qian Correction to: A Finite
Element/Operator-Splitting Method for
the Numerical Solution of the Two
Dimensional Elliptic Monge--Amp\`ere
Equation . . . . . . . . . . . . . . . . 48--48
Ricardo Oyarzúa and
Manuel Solano and
Paulo Zúñiga A High Order Mixed-FEM for Diffusion
Problems on Curved Domains . . . . . . . 49--78
Praveen Chandrashekar A Global Divergence Conforming DG Method
for Hyperbolic Conservation Laws with
Divergence Constraint . . . . . . . . . 79--102
Luisa Fermo and
Maria Grazia Russo and
Giada Serafini Numerical Methods for Cauchy Bisingular
Integral Equations of the First Kind on
the Square . . . . . . . . . . . . . . . 103--127
Jian-Feng Cai and
Haixia Liu and
Yang Wang Fast Rank-One Alternating Minimization
Algorithm for Phase Retrieval . . . . . 128--147
Ruchi Guo and
Tao Lin and
Yanping Lin A Fixed Mesh Method with Immersed Finite
Elements for Solving Interface Inverse
Problems . . . . . . . . . . . . . . . . 148--175
L. Freret and
L. Ivan and
H. De Sterck and
C. P. T. Groth High-Order Finite-Volume Method with
Block-Based AMR for Magnetohydrodynamics
Flows . . . . . . . . . . . . . . . . . 176--208
Mark Ainsworth and
Guosheng Fu Dispersive Behavior of an
Energy-Conserving Discontinuous Galerkin
Method for the One-Way Wave Equation . . 209--226
Daniel Baffet A Gauss--Jacobi Kernel Compression
Scheme for Fractional Differential
Equations . . . . . . . . . . . . . . . 227--248
J. Glaubitz and
A. C. Nogueira, Jr. and
J. L. S. Almeida and
R. F. Cantão and
C. A. C. Silva Smooth and Compactly Supported Viscous
Sub-cell Shock Capturing for
Discontinuous Galerkin Methods . . . . . 249--272
C. Escalante and
E. D. Fernández-Nieto and
T. Morales de Luna and
M. J. Castro An Efficient Two-Layer Non-hydrostatic
Approach for Dispersive Water Waves . . 273--320
S. De Marchi and
A. Martínez and
E. Perracchione and
M. Rossini RBF-Based Partition of Unity Methods for
Elliptic PDEs: Adaptivity and Stability
Issues Via Variably Scaled Kernels . . . 321--344
Zhenzhu Chen and
Yunfeng Xiong and
Sihong Shao Numerical Methods for the Wigner
Equation with Unbounded Potential . . . 345--368
Hsueh-Chen Lee and
Hyesuk Lee Numerical Simulations of Viscoelastic
Fluid Flows Past a Transverse Slot Using
Least-Squares Finite Element Methods . . 369--388
Li Shan and
Jiangyong Hou and
Wenjing Yan and
Jie Chen Partitioned Time Stepping Method for a
Dual-Porosity-Stokes Model . . . . . . . 389--413
G. Murali Mohan Reddy and
Rajen Kumar Sinha and
José Alberto Cuminato A Posteriori Error Analysis of the
Crank--Nicolson Finite Element Method
for Parabolic Integro--Differential
Equations . . . . . . . . . . . . . . . 414--441
Tao Lin and
Dongwoo Sheen and
Xu Zhang A Nonconforming Immersed Finite Element
Method for Elliptic Interface Problems 442--463
Yedan Shen and
Yang Kuang and
Guanghui Hu An Asymptotics-Based Adaptive Finite
Element Method for Kohn--Sham Equation 464--492
Vahid Mohammadi and
Davoud Mirzaei and
Mehdi Dehghan Numerical Simulation and Error
Estimation of the Time-Dependent
Allen--Cahn Equation on Surfaces with
Radial Basis Functions . . . . . . . . . 493--516
Huan Li and
Zhouchen Lin Accelerated Alternating Direction Method
of Multipliers: an Optimal $O$ (1 40/40
$K$ ) Nonergodic Analysis . . . . . . . 671--699
Zhaopeng Hao and
Moongyu Park and
Guang Lin and
Zhiqiang Cai Finite Element Method for Two-Sided
Fractional Differential Equations with
Variable Coefficients: Galerkin Approach 700--717
Santiago Badia and
Alberto F. Martín and
Hieu Nguyen Physics-Based Balancing Domain
Decomposition by Constraints for
Multi-Material Problems . . . . . . . . 718--747
Peter Korn A Regularity-Aware Algorithm for
Variational Data Assimilation of an
Idealized Coupled Atmosphere--Ocean
Model . . . . . . . . . . . . . . . . . 748--786
Shaobo Wang and
Shidong Jiang and
Jing Wang Fast High-Order Integral Equation
Methods for Solving Boundary Value
Problems of Two Dimensional Heat
Equation in Complex Geometry . . . . . . 787--808
Xue Zhang and
Xiaoqun Zhang A New Proximal Iterative Hard
Thresholding Method with Extrapolation
for $ \ell_0 $ Minimization . . . . . . 809--826
Marius Oltean and
Carlos F. Sopuerta and
Alessandro D. A. M. Spallicci Particle-without-Particle: a Practical
Pseudospectral Collocation Method for
Linear Partial Differential Equations
with Distributional Sources . . . . . . 827--866
Francisco Bernal An Implementation of Milstein's Method
for General Bounded Diffusions . . . . . 867--890
Jianfang Lin and
Rémi Abgrall and
Jianxian Qiu High Order Residual Distribution for
Steady State Problems for Hyperbolic
Conservation Laws . . . . . . . . . . . 891--913
Qilong Zhai and
Hehu Xie and
Ran Zhang and
Zhimin Zhang Acceleration of Weak Galerkin Methods
for the Laplacian Eigenvalue Problem . . 914--934
F. Hecht and
Z. Mghazli and
I. Naji and
J. E. Roberts A Residual a Posteriori Error Estimators
for a Model for Flow in Porous Media
with Fractures . . . . . . . . . . . . . 935--968
Yana Di and
Yuwei Fan and
Zhenzhong Kou and
Ruo Li and
Yanli Wang Filtered Hyperbolic Moment Method for
the Vlasov Equation . . . . . . . . . . 969--991
F. X. Trias and
D. Folch and
A. Gorobets and
A. Oliva Spectrally-Consistent Regularization of
Navier--Stokes Equations . . . . . . . . 992--1014
Juntao Huang and
Weifeng Zhao and
Chi-Wang Shu A Third-Order Unconditionally
Positivity--Preserving Scheme for
Production--Destruction Equations with
Applications to Non-equilibrium Flows 1015--1056
Wenli Yang and
Zhongyi Huang and
Wei Zhu Image Segmentation Using the
Cahn--Hilliard Equation . . . . . . . . 1057--1077
Haiyan Su and
Shipeng Mao and
Xinlong Feng Optimal Error Estimates of Penalty Based
Iterative Methods for Steady
Incompressible Magnetohydrodynamics
Equations with Different Viscosities . . 1078--1110
Xiaofeng Cai and
Wei Guo and
Jing-Mei Qiu A High Order Semi-Lagrangian
Discontinuous Galerkin Method for the
Two-Dimensional Incompressible Euler
Equations and the Guiding Center Vlasov
Model Without Operator Splitting . . . . 1111--1134
Alan Ayala and
Xavier Claeys and
Laura Grigori ALORA: Affine Low-Rank Approximations 1135--1160
Thomas Führer and
Norbert Heuer Optimal Quasi-diagonal Preconditioners
for Pseudodifferential Operators of
Order Minus Two . . . . . . . . . . . . 1161--1181
Yingxiang Xu and
Xin Chen Optimized Schwarz Methods for the
Optimal Control of Systems Governed by
Elliptic Partial Differential Equations 1182--1213
Maojun Li and
Haiyun Dong and
Binbin Hu and
Liwei Xu Maximum-Principle-Satisfying and
Positivity-Preserving High Order Central
DG Methods on Unstructured Overlapping
Meshes for Two-Dimensional Hyperbolic
Conservation Laws . . . . . . . . . . . 1361--1388
David A. Kopriva and
Florian J. Hindenlang and
Thomas Bolemann and
Gregor J. Gassner Free-Stream Preservation for Curved
Geometrically Non-conforming
Discontinuous Galerkin Spectral Elements 1389--1408
Jie Yang and
Weidong Zhao and
Tao Zhou Explicit Deferred Correction Methods for
Second-Order Forward Backward Stochastic
Differential Equations . . . . . . . . . 1409--1432
G. Perrin and
G. Defaux Efficient Evaluation of
Reliability--Oriented Sensitivity
Indices . . . . . . . . . . . . . . . . 1433--1455
Dongping Qi and
Alexander Vladimirsky Corner Cases, Singularities, and Dynamic
Factoring . . . . . . . . . . . . . . . 1456--1476
S. Herrmann and
C. Zucca Exact Simulation of the First-Passage
Time of Diffusions . . . . . . . . . . . 1477--1504
Manuel Solano and
Felipe Vargas A High Order HDG Method for Stokes Flow
in Curved Domains . . . . . . . . . . . 1505--1533
Weinan E and
Martin Hutzenthaler and
Arnulf Jentzen and
Thomas Kruse On Multilevel Picard Numerical
Approximations for High-Dimensional
Nonlinear Parabolic Partial Differential
Equations and High-Dimensional Nonlinear
Backward Stochastic Differential
Equations . . . . . . . . . . . . . . . 1534--1571
Philipp Öffner and
Hendrik Ranocha Error Boundedness of Discontinuous
Galerkin Methods with Variable
Coefficients . . . . . . . . . . . . . . 1572--1607
Xiang Wang and
Xing Li and
Lei-Hong Zhang and
Ren-Cang Li An Efficient Numerical Method for the
Symmetric Positive Definite Second-Order
Cone Linear Complementarity Problem . . 1608--1629
Hao Dong and
Xiaojing Zheng and
Junzhi Cui and
Yufeng Nie and
Zhiqiang Yang and
Zihao Yang Multiscale Computational Method for
Dynamic Thermo-Mechanical Problems of
Composite Structures with Diverse
Periodic Configurations in Different
Subdomains . . . . . . . . . . . . . . . 1630--1666
Quentin Chan-Wai-Nam and
Joseph Mikael and
Xavier Warin Machine Learning for Semi Linear PDEs 1667--1712
Yu Du and
Zhimin Zhang Supercloseness of Linear DG--FEM and Its
Superconvergence Based on the Polynomial
Preserving Recovery for Helmholtz
Equation . . . . . . . . . . . . . . . . 1713--1736
Guosheng Fu An Explicit Divergence-Free DG Method
for Incompressible Magnetohydrodynamics 1737--1752
Jianqiang Xie and
Zhiyue Zhang An Effective Dissipation-Preserving
Fourth-Order Difference Solver for
Fractional-in-Space Nonlinear Wave
Equations . . . . . . . . . . . . . . . 1753--1776
Bernardo Cockburn and
John R. Singler and
Yangwen Zhang Interpolatory HDG Method for Parabolic
Semilinear PDEs . . . . . . . . . . . . 1777--1800
Yunxia Wei and
Yanping Chen A Jacobi Spectral Method for Solving
Multidimensional Linear Volterra
Integral Equation of the Second Kind . . 1801--1813
J. Liu and
J. Sun and
T. Turner Spectral Indicator Method for a
Non-selfadjoint Steklov Eigenvalue
Problem . . . . . . . . . . . . . . . . 1814--1831
Carlos Lozano Entropy Production by Implicit
Runge--Kutta Schemes . . . . . . . . . . 1832--1853
Saeed Ghadimi and
Guanghui Lan and
Hongchao Zhang Generalized Uniformly Optimal Methods
for Nonlinear Programming . . . . . . . 1854--1881
Hong-lin Liao and
Yonggui Yan and
Jiwei Zhang Unconditional Convergence of a Fast
Two-Level Linearized Algorithm for
Semilinear Subdiffusion Equations . . . 1--25
Yekaterina Epshteyn and
Qing Xia Efficient Numerical Algorithms Based on
Difference Potentials for Chemotaxis
Systems in 3D . . . . . . . . . . . . . 26--59
Fang Feng and
Weimin Han and
Jianguo Huang Virtual Element Methods for Elliptic
Variational Inequalities of the Second
Kind . . . . . . . . . . . . . . . . . . 60--80
Hengfei Ding and
Changpin Li A High-0rder Algorithm for
Time-Caputo-Tempered Partial
Differential Equation with Riesz
Derivatives in Two Spatial Dimensions 81--109
Ehsan Kharazmi and
Mohsen Zayernouri Fractional Sensitivity Equation Method:
Application to Fractional Model
Construction . . . . . . . . . . . . . . 110--140
Mario Alvarez and
Gabriel N. Gatica and
Bryan Gomez-Vargas and
Ricardo Ruiz-Baier New Mixed Finite Element Methods for
Natural Convection with Phase-Change in
Porous Media . . . . . . . . . . . . . . 141--174
Lucas Friedrich and
Gero Schnücke and
Andrew R. Winters and
David C. Del Rey Fernández and
Gregor J. Gassner and
Mark H. Carpenter Entropy Stable Space--Time Discontinuous
Galerkin Schemes with Summation-by-Parts
Property for Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 175--222
Guangpu Zhu and
Jisheng Kou and
Shuyu Sun and
Jun Yao and
Aifen Li Numerical Approximation of a Phase-Field
Surfactant Model with Fluid Flow . . . . 223--247
Zhiwei Fang and
Jichun Li and
Tao Tang and
Tao Zhou Efficient Stochastic Galerkin Methods
for Maxwell's Equations with Random
Inputs . . . . . . . . . . . . . . . . . 248--267
Ruo Li and
Pingbing Ming and
Ziyuan Sun and
Zhijian Yang An Arbitrary-Order Discontinuous
Galerkin Method with One Unknown Per
Element . . . . . . . . . . . . . . . . 268--288
Arturo Vargas and
Thomas Hagstrom and
Jesse Chan and
Tim Warburton Leapfrog Time-Stepping for Hermite
Methods . . . . . . . . . . . . . . . . 289--314
Nan Jiang A Pressure-Correction Ensemble Scheme
for Computing Evolutionary Boussinesq
Equations . . . . . . . . . . . . . . . 315--350
Max Jensen and
Ananta K. Majee and
Andreas Prohl and
Christian Schellnegger Dynamic Programming for Finite Ensembles
of Nanomagnetic Particles . . . . . . . 351--375
Will Pazner and
Per-Olof Persson Analysis and Entropy Stability of the
Line-Based Discontinuous Galerkin Method 376--402
Dongfang Li and
Chengda Wu and
Zhimin Zhang Linearized Galerkin FEMs for Nonlinear
Time Fractional Parabolic Problems with
Non-smooth Solutions in Time Direction 403--419
Gang Chen and
Peter Monk and
Yangwen Zhang An HDG Method for the Time-dependent
Drift--Diffusion Model of Semiconductor
Devices . . . . . . . . . . . . . . . . 420--443
Andreas Prohl and
Christian Schellnegger Adaptive Concepts for Stochastic Partial
Differential Equations . . . . . . . . . 444--474
N. K. Yadav and
J. H. M. ten Thije Boonkkamp and
W. L. IJzerman A Monge--Amp\`ere Problem with
Non-quadratic Cost Function to Compute
Freeform Lens Surfaces . . . . . . . . . 475--499
Xiaobo Jing and
Jun Li and
Xueping Zhao and
Qi Wang Second Order Linear Energy Stable
Schemes for Allen--Cahn Equations with
Nonlocal Constraints . . . . . . . . . . 500--537
Yuanzhen Cheng and
Alina Chertock and
Michael Herty and
Alexander Kurganov and
Tong Wu A New Approach for Designing
Moving-Water Equilibria Preserving
Schemes for the Shallow Water Equations 538--554
Beiping Duan and
Zhoushun Zheng An Exponentially Convergent Scheme in
Time for Time Fractional Diffusion
Equations with Non-smooth Initial Data 717--742
Ashok Jallepalli and
Robert M. Kirby Efficient Algorithms for the Line-SIAC
Filter . . . . . . . . . . . . . . . . . 743--761
Victor Churchill and
Anne Gelb Detecting Edges from Non-uniform Fourier
Data via Sparse Bayesian Learning . . . 762--783
I. Higueras and
T. Roldán Strong Stability Preserving Properties
of Composition Runge--Kutta Schemes . . 784--807
Matthew Jacobs and
Songting Luo Asymptotic Solutions for High Frequency
Helmholtz Equations in Anisotropic Media
with Hankel Functions . . . . . . . . . 808--833
Shinya Uchiumi A Viscosity-Independent Error Estimate
of a Pressure-Stabilized
Lagrange--Galerkin Scheme for the Oseen
Problem . . . . . . . . . . . . . . . . 834--858
Mi-Song Dupuy Discretization Error Cancellation in the
Plane-Wave Approximation of Periodic
Hamiltonians with Coulomb Singularities 859--877
Maximilian Bremer and
Kazbek Kazhyken and
Hartmut Kaiser and
Craig Michoski and
Clint Dawson Performance Comparison of HPX Versus
Traditional Parallelization Strategies
for the Discontinuous Galerkin Method 878--902
Chengda Wu and
Weiwei Sun New Analysis of Galerkin FEMs for
Miscible Displacement in Porous Media 903--923
Christophe Berthon and
Arnaud Duran and
Françoise Foucher and
Khaled Saleh and
Jean De Dieu Zabsonré Improvement of the Hydrostatic
Reconstruction Scheme to Get Fully
Discrete Entropy Inequalities . . . . . 924--956
Hao Luo and
Binjie Li and
Xiaoping Xie Convergence Analysis of a
Petrov--Galerkin Method for Fractional
Wave Problems with Nonsmooth Data . . . 957--992
Chenyang Zhang and
Huipo Liu and
Zhaojie Zhou A Priori Error Analysis for
Time-Stepping Discontinuous Galerkin
Finite Element Approximation of Time
Fractional Optimal Control Problem . . . 993--1018
Weifeng Qiu and
Ke Shi Analysis on an HDG Method for the
$p$-Laplacian Equations . . . . . . . . 1019--1032
Xu Chen and
Si-Wen Deng and
Siu-Long Lei A Robust Preconditioner for
Two-dimensional Conservative
Space--Fractional Diffusion Equations on
Convex Domains . . . . . . . . . . . . . 1033--1057
David Shepherd and
James Miles and
Matthias Heil and
Milan Mihajlovi\'c An Adaptive Step Implicit Midpoint Rule
for the Time Integration of Newton's
Linearisations of Non-Linear Problems
with Applications in Micromagnetics . . 1058--1082
Huadong Gao and
Lili Ju and
Wen Xie A Stabilized Semi-Implicit Euler
Gauge-Invariant Method for the
Time-Dependent Ginzburg--Landau
Equations . . . . . . . . . . . . . . . 1083--1115
Yan-Fei Xiang and
Yan-Fei Jing and
Ting-Zhu Huang A New Projected Variant of the Deflated
Block Conjugate Gradient Method . . . . 1116--1138
Honglin Yuan and
Xiaoyi Gu and
Rongjie Lai and
Zaiwen Wen Global Optimization with Orthogonality
Constraints via Stochastic Diffusion on
Manifold . . . . . . . . . . . . . . . . 1139--1170
Ruisheng Qi and
Xiaojie Wang Optimal Error Estimates of Galerkin
Finite Element Methods for Stochastic
Allen--Cahn Equation with Additive Noise 1171--1194
Yat Tin Chow and
Wuchen Li and
Stanley Osher and
Wotao Yin Algorithm for Hamilton--Jacobi Equations
in Density Space Via a Generalized Hopf
Formula . . . . . . . . . . . . . . . . 1195--1239
Larry L. Schumaker Solving Elliptic PDE's on Domains with
Curved Boundaries with an Immersed
Penalized Boundary Method . . . . . . . 1369--1394
Xiangcheng Zheng and
Huan Liu and
Hong Wang and
Hongfei Fu An Efficient Finite Volume Method for
Nonlinear Distributed-Order
Space-Fractional Diffusion Equations in
Three Space Dimensions . . . . . . . . . 1395--1418
Francesca Arrigo and
Desmond J. Higham and
Vanni Noferini Non-backtracking PageRank . . . . . . . 1419--1437
Duong Viet Thong and
Nguyen The Vinh and
Yeol Je Cho Accelerated Subgradient Extragradient
Methods for Variational Inequality
Problems . . . . . . . . . . . . . . . . 1438--1462
Christiane Helzel and
David Kerkmann and
Leonardo Scandurra A New ADER Method Inspired by the Active
Flux Method . . . . . . . . . . . . . . 1463--1497
Xiaobing Feng and
Junshan Lin and
Cody Lorton A Multi-modes Monte Carlo Interior
Penalty Discontinuous Galerkin Method
for the Time-Harmonic Maxwell's
Equations with Random Coefficients . . . 1498--1528
Haotao Cai A Fractional Spectral Collocation for
Solving Second Kind Nonlinear Volterra
Integral Equations with Weakly Singular
Kernels . . . . . . . . . . . . . . . . 1529--1548
Michael A. Puthawala and
Cory D. Hauck and
Stanley J. Osher Diagnosing Forward Operator Error Using
Optimal Transport . . . . . . . . . . . 1549--1576
V. Anaya and
A. Bouharguane and
D. Mora and
C. Reales and
R. Ruiz-Baier and
N. Seloula and
H. Torres Analysis and Approximation of a
Vorticity--Velocity--Pressure
Formulation for the Oseen Equations . . 1577--1606
Pin Lyu and
Seakweng Vong A High-Order Method with a Temporal
Nonuniform Mesh for a Time-Fractional
Benjamin--Bona--Mahony Equation . . . . 1607--1628
Chaolong Jiang and
Wenjun Cai and
Yushun Wang A Linearly Implicit and Local
Energy-Preserving Scheme for the
Sine--Gordon Equation Based on the
Invariant Energy Quadratization Approach 1629--1655
Xiang Xu and
Yanxiang Zhao Energy Stable Semi-implicit Schemes for
Allen--Cahn--Ohta--Kawasaki Model in
Binary System . . . . . . . . . . . . . 1656--1680
Yaning Xie and
Wenjun Ying and
Wei-Cheng Wang A High-Order Kernel-Free Boundary
Integral Method for the Biharmonic
Equation on Irregular Domains . . . . . 1681--1699
William F. Mitchell and
John S. Villarrubia An a Posteriori Error Estimate for
Scanning Electron Microscope Simulation
with Adaptive Mesh Refinement . . . . . 1700--1715
Wenbin Chen and
Yichao Zhang and
Weijia Li and
Yanqiu Wang and
Yue Yan Optimal Convergence Analysis of a Second
Order Scheme for a Thin Film Model
Without Slope Selection . . . . . . . . 1716--1730
Lot-Kei Chou and
Siu-Long Lei Tensor-Train Format Solution with
Preconditioned Iterative Method for High
Dimensional Time-Dependent
Space-Fractional Diffusion Equations
with Error Analysis . . . . . . . . . . 1731--1763
Adrian M. Ruf and
Espen Sande and
Susanne Solem The Optimal Convergence Rate of Monotone
Schemes for Conservation Laws in the
Wasserstein Distance . . . . . . . . . . 1764--1776
J. A. Carrillo and
N. Kolbe and
M. Lukácová-Medvid'ová A Hybrid Mass Transport Finite Element
Method for Keller--Segel Type Systems 1777--1804
Gianmarco Manzini and
Gianluca Maguolo and
Mario Putti The High-Order Mixed Mimetic Finite
Difference Method for Time-Dependent
Diffusion Problems . . . . . . . . . . . 1805--1830
Gianmarco Manzini and
Gianluca Maguolo and
Mario Putti Correction to: The High-Order Mixed
Mimetic Finite Difference Method for
Time-Dependent Diffusion Problems . . . 1831--1831
Tony Leli\`evre and
Simona Perotto and
Gianluigi Rozza and
Daniele A. Di Pietro and
Alexandre Ern and
Luca Formaggia Preface: Special Issue on Model
Reduction . . . . . . . . . . . . . . . 1--2
Babak Maboudi Afkham and
Jan S. Hesthaven Structure-Preserving Model-Reduction of
Dissipative Hamiltonian Systems . . . . 3--21
José V. Aguado and
Domenico Borzacchiello and
Kiran S. Kollepara and
Francisco Chinesta and
Antonio Huerta Tensor Representation of Non-linear
Models Using Cross Approximations . . . 22--47
Bachmann Freya and
Beermann Dennis and
Lu Jianjie and
Volkwein Stefan POD-Based Mixed-Integer Optimal Control
of the Heat Equation . . . . . . . . . . 48--75
Max Gunzburger and
Michael Schneier and
Clayton Webster and
Guannan Zhang An Improved Discrete
Least-Squares/Reduced-Basis Method for
Parameterized Elliptic PDEs . . . . . . 76--91
Kenan Kergrene and
Ludovic Chamoin and
Marc Laforest and
Serge Prudhomme On a Goal-Oriented Version of the Proper
Generalized Decomposition Method . . . . 92--111
Federico Pichi and
Gianluigi Rozza Reduced Basis Approaches for
Parametrized Bifurcation Problems held
by Non-linear Von Kármán Equations . . . . 112--135
Luca Venturi and
Francesco Ballarin and
Gianluigi Rozza A Weighted POD Method for Elliptic PDEs
with Random Inputs . . . . . . . . . . . 136--153
Kelong Cheng and
Zhonghua Qiao and
Cheng Wang A Third Order Exponential Time
Differencing Numerical Scheme for
No-Slope-Selection Epitaxial Thin Film
Model with Energy Stability . . . . . . 154--185
Jiong Ren and
Gang Wang and
Mingsheng Ma A Group of CFL-Dependent Flux-Limiters
to Control the Numerical Dissipation in
Multi-stage Unsteady Calculation . . . . 186--216
Hyuntae Cho and
Heejae Han and
Byungjoon Lee and
Youngsoo Ha and
Myungjoo Kang A Second-Order Boundary Condition
Capturing Method for Solving the
Elliptic Interface Problems on Irregular
Domains . . . . . . . . . . . . . . . . 217--251
Guojian Yin A Contour-Integral Based Method with
Schur--Rayleigh--Ritz Procedure for
Generalized Eigenvalue Problems . . . . 252--270
Pranjal and
David Silvester Balanced Iterative Solvers for Linear
Nonsymmetric Systems and Nonlinear
Systems with PDE Origins: Efficient
Black--Box Stopping Criteria . . . . . . 271--290
Peipei Lu and
Xuejun Xu A Robust Multilevel Preconditioner Based
on a Domain Decomposition Method for the
Helmholtz Equation . . . . . . . . . . . 291--311
Mekki Ayadi and
Hela Ayed and
Leonardo Baffico and
Taoufik Sassi Stokes Problem with Slip Boundary
Conditions of Friction Type: Error
Analysis of a Four-Field Mixed
Variational Formulation . . . . . . . . 312--341
Nan Wang and
Jinru Chen A Nonconforming Nitsche's Extended
Finite Element Method for Stokes
Interface Problems . . . . . . . . . . . 342--374
Meng Chen and
Leevan Ling Kernel-Based Meshless Collocation
Methods for Solving Coupled Bulk-Surface
Partial Differential Equations . . . . . 375--391
Afsaneh Moradi and
Javad Farzi and
Ali Abdi Strong Stability Preserving Second
Derivative General Linear Methods . . . 392--435
Dongdong He and
Kejia Pan and
Xiaoqiang Yue A Positivity Preserving and Free Energy
Dissipative Difference Scheme for the
Poisson--Nernst--Planck System . . . . . 436--458
Jesse Chan Skew-Symmetric Entropy Stable Modal
Discontinuous Galerkin Formulations . . 459--485
Gang Chen and
Guosheng Fu and
John R. Singler and
Yangwen Zhang A Class of Embedded DG Methods for
Dirichlet Boundary Control of Convection
Diffusion PDEs . . . . . . . . . . . . . 623--648
Guo-Yan Zhao and
Ming-Bo Sun and
Yong Mei and
Liang Li and
Hong-Bo Wang and
Guang-Xin Li and
Yuan Liu and
Yong-Chao Sun and
Chang-Hai Liang An Efficient Adaptive Central-Upwind
WENO--CU6 Numerical Scheme with a New
Sensor . . . . . . . . . . . . . . . . . 649--670
Nattaporn Chuenjarern and
Yang Yang Fourier Analysis of Local Discontinuous
Galerkin Methods for Linear Parabolic
Equations on Overlapping Meshes . . . . 671--688
Qiang Ma and
Hao Wang and
Zhiqiang Yang and
Zhihui Li and
Junzhi Cui Second-Order Asymptotic Analysis and
Computations of Axially and Spherically
Symmetric Piezoelectric Problems for
Composite Structures . . . . . . . . . . 689--731
U. S. Vevek and
B. Zang and
T. H. New An Efficient Hybrid Method for Solving
Euler Equations . . . . . . . . . . . . 732--762
Weiyang Ding and
Michael K. Ng and
Wenxing Zhang A Peaceman--Rachford Splitting Method
with Monotone Plus Skew-Symmetric
Splitting for Nonlinear Saddle Point
Problems . . . . . . . . . . . . . . . . 763--788
Hailiang Liu and
Peimeng Yin Unconditionally Energy Stable DG Schemes
for the Swift--Hohenberg Equation . . . 789--819
Marvin Bohm and
Sven Schermeng and
Andrew R. Winters and
Gregor J. Gassner and
Gustaaf B. Jacobs Multi-element SIAC Filter for Shock
Capturing Applied to High-Order
Discontinuous Galerkin Spectral Element
Methods . . . . . . . . . . . . . . . . 820--844
Sudeep Kundu and
Amiya Kumar Pani Global Stabilization of BBM--Burgers'
Type Equations by Nonlinear Boundary
Feedback Control Laws: Theory and Finite
Element Error Analysis . . . . . . . . . 845--880
Keegan L. A. Kirk and
Sander Rhebergen Analysis of a Pressure-Robust Hybridized
Discontinuous Galerkin Method for the
Stationary Navier--Stokes Equations . . 881--897
Yahui Wang and
Yulong Du and
Kunlei Zhao and
Li Yuan Modified Stencil Approximations for
Fifth-Order Weighted Essentially
Non-oscillatory Schemes . . . . . . . . 898--922
Zheng Li and
Guohui Song and
Yuesheng Xu A Two-Step Fixed-Point Proximity
Algorithm for a Class of
Non-differentiable Optimization Models
in Machine Learning . . . . . . . . . . 923--940
Meng Ding and
Ting-Zhu Huang and
Teng-Yu Ji and
Xi-Le Zhao and
Jing-Hua Yang Low-Rank Tensor Completion Using Matrix
Factorization Based on Tensor Train Rank
and Total Variation . . . . . . . . . . 941--964
Shuying Zhai and
Dongling Wang and
Zhifeng Weng and
Xuan Zhao Error Analysis and Numerical Simulations
of Strang Splitting Method for Space
Fractional Nonlinear Schrödinger Equation 965--989
L. Beirão da Veiga and
D. Mora and
G. Vacca The Stokes Complex for Virtual Elements
with Application to Navier--Stokes Flows 990--1018
S. Bertoluzza and
S. Falletta FEM Solution of Exterior Elliptic
Problems with Weakly Enforced Integral
Non Reflecting Boundary Conditions . . . 1019--1049
Jan Nordström and
Andrea A. Ruggiu Dual Time-Stepping Using Second
Derivatives . . . . . . . . . . . . . . 1050--1071
Hehu Xie and
Manting Xie Computable Error Estimates for Ground
State Solution of Bose--Einstein
Condensates . . . . . . . . . . . . . . 1072--1087
Jie Shen and
Chang-Tao Sheng An Efficient Space--Time Method for Time
Fractional Diffusion Equation . . . . . 1088--1110
Markus Wahlsten and
Jan Nordström On Stochastic Investigation of Flow
Problems Using the Viscous Burgers'
Equation as an Example . . . . . . . . . 1111--1117
Alina Chertock and
Adi Ditkowski and
Anne Gelb and
Sigal Gottlieb and
Semyon Tsynkov Preface to the Special Issue in Memory
of Professor Saul Abarbanel . . . . . . 1119--1123
Bertil Gustafsson Saul Abarbanel; Half a Century of
Scientific Work . . . . . . . . . . . . 1124--1135
V. S. Ryaben'kii and
V. A. Torgashov An Iteration-Free Approach to Solving
the Navier--Stokes Equations by Implicit
Finite Difference Schemes in the
Vorticity-Stream Function Formulation 1136--1149
Xiaozhou Li and
Jennifer K. Ryan and
Robert M. Kirby and
Kees Vuik Smoothness-Increasing
Accuracy-Conserving (SIAC) Filtering for
Discontinuous Galerkin Solutions over
Nonuniform Meshes: Superconvergence and
Optimal Accuracy . . . . . . . . . . . . 1150--1180
F. Smith and
S. Tsynkov and
E. Turkel Compact High Order Accurate Schemes for
the Three Dimensional Wave Equation . . 1181--1209
Yong Liu and
Tianheng Chen and
Yanlai Chen and
Chi-Wang Shu Certified Offline-Free Reduced Basis
(COFRB) Methods for Stochastic
Differential Equations Driven by
Arbitrary Types of Noise . . . . . . . . 1210--1239
Anne Gelb and
X. Hou and
Q. Li Numerical Analysis for Conservation Laws
Using $ l_1 $ Minimization . . . . . . . 1240--1265
Michael Sever A Source of Uncertainty in Computed
Discontinuous Flows . . . . . . . . . . 1266--1296
Xin Liu and
Alina Chertock and
Alexander Kurganov and
Karlan Wolfkill One-Dimensional/Two-Dimensional Coupling
Approach with Quadrilateral Confluence
Region for Modeling River Systems . . . 1297--1328
Yinghua Wang and
Bao-Shan Wang and
Wai Sun Don Generalized Sensitivity Parameter Free
Fifth Order WENO Finite Difference
Scheme with $Z$-Type Weights . . . . . . 1329--1358
Björn Sjögreen and
H. C. Yee Entropy Stable Method for the Euler
Equations Revisited: Central
Differencing via Entropy Splitting and
SBP . . . . . . . . . . . . . . . . . . 1359--1385
Matania Ben-Artzi and
Jean-Pierre Croisille and
Dalia Fishelov A Cartesian Compact Scheme for the
Navier--Stokes Equations in
Streamfunction Formulation in Irregular
Domains . . . . . . . . . . . . . . . . 1386--1408
O. Peles and
E. Turkel Adaptive Time Steps for Compressible
Flows Based on Dual-Time Stepping and a
RK/Implicit Smoother . . . . . . . . . . 1409--1428
Jiah Song and
Smadar Karni A Second Order Traffic Flow Model with
Lane Changing . . . . . . . . . . . . . 1429--1445
Leah Isherwood and
Zachary J. Grant and
Sigal Gottlieb Strong Stability Preserving Integrating
Factor Two-Step Runge--Kutta Methods . . 1446--1471
Isaac Harari and
Uri Albocher Complementary Solutions of Nitsche's
Method . . . . . . . . . . . . . . . . . 1472--1492
A. Y. Meltzer An Accurate Approximation of Exponential
Integrators for the Schrödinger Equation 1493--1508
T. Hagstrom and
J. W. Banks and
B. B. Buckner and
K. Juhnke Discontinuous Galerkin Difference
Methods for Symmetric Hyperbolic Systems 1509--1526
Chaoxu Pei and
Mehdi Vahab and
Mark Sussman and
M. Yousuff Hussaini A Hierarchical Space--Time Spectral
Element and Moment-of-Fluid Method for
Improved Capturing of Vortical
Structures in Incompressible
Multi-phase/Multi-material Flows . . . . 1527--1566
Kao-Pu Chang and
Jessica M. Libertini and
Steven Seay Comparing Gradient Descent with
Automatic Differentiation and Particle
Swarm Optimization Techniques for
Estimating Tumor Blood Flow Parameters
in Contrast-Enhanced Imaging . . . . . . 1567--1576
Yize Yu and
Yan Jiang and
Mengping Zhang Free-Stream Preserving Finite Difference
Schemes for Ideal Magnetohydrodynamics
on Curvilinear Meshes . . . . . . . . . ??
Anqi Chen and
Yingda Cheng and
Yong Liu and
Mengping Zhang Superconvergence of Ultra-Weak
Discontinuous Galerkin Methods for the
Linear Schrödinger Equation in One
Dimension . . . . . . . . . . . . . . . ??
Qianqian Ding and
Shipeng Mao A Convergent Finite Element Method for
the Compressible Magnetohydrodynamics
System . . . . . . . . . . . . . . . . . ??
Fei Xu and
Qiumei Huang Local and Parallel Multigrid Method for
Nonlinear Eigenvalue Problems . . . . . ??
Wenrui Hao and
Jan Hesthaven and
Guang Lin and
Bin Zheng A Homotopy Method with Adaptive Basis
Selection for Computing Multiple
Solutions of Differential Equations . . ??
Xue-Li Li and
Yu-Xin Ren High Order Compact Generalized Finite
Difference Methods for Solving Inviscid
Compressible Flows . . . . . . . . . . . ??
Sheng Chen and
Jie Shen An Efficient and Accurate Numerical
Method for the Spectral Fractional
Laplacian Equation . . . . . . . . . . . ??
Tomas Lundquist and
Jan Nordström Stable and Accurate Filtering Procedures ??
Asha Kumari Meena and
Rakesh Kumar and
Praveen Chandrashekar Positivity-Preserving Finite Difference
WENO Scheme for Ten-Moment Equations
with Source Term . . . . . . . . . . . . ??
Adam Oberman and
Tiago Salvador A Partial Differential Equation Obstacle
Problem for the Level Set Approach to
Visibility . . . . . . . . . . . . . . . ??
Mahmoud A. Zaky and
Ahmed S. Hendy and
Jorge E. Macías-Díaz Semi-implicit Galerkin--Legendre
Spectral Schemes for Nonlinear
Time-Space Fractional
Diffusion--Reaction Equations with
Smooth and Nonsmooth Solutions . . . . . ??
Lina Zhao and
Eun-Jae Park A New Hybrid Staggered Discontinuous
Galerkin Method on General Meshes . . . ??
Shangqi Gao and
Qibin Fan Robust Schatten-p Norm Based Approach
for Tensor Completion . . . . . . . . . ??
Chaobao Huang and
Martin Stynes Superconvergence of a Finite Element
Method for the Multi-term
Time-Fractional Diffusion Problem . . . ??
Wei Liu and
Jintao Cui and
Zhifeng Wang A New Numerical Method for an Asymptotic
Coupled Model of Fractured Media Aquifer
System . . . . . . . . . . . . . . . . . ??
Zhijie Du and
Huoyuan Duan A Mixed Method for Maxwell Eigenproblem ??
P. O. Olatunji and
M. N. O. Ikhile Strongly Regular General Linear Methods ??
A. Faghih and
P. Mokhtary An Efficient Formulation of Chebyshev
Tau Method for Constant Coefficients
Systems of Multi-order FDEs . . . . . . ??
Ming Cui and
Shangyou Zhang On the Uniform Convergence of the Weak
Galerkin Finite Element Method for a
Singularly-Perturbed Biharmonic Equation ??
Binjie Li and
Tao Wang and
Xiaoping Xie Analysis of a Time-Stepping
Discontinuous Galerkin Method for
Fractional Diffusion-Wave Equations with
Nonsmooth Data . . . . . . . . . . . . . ??
Jason E. Hicken Entropy-Stable, High-Order
Summation-by-Parts Discretizations
Without Interface Penalties . . . . . . ??
Thomas P. Wihler and
Marcel Wirz Stability and Convergence of Spectral
Mixed Discontinuous Galerkin Methods for
$3$D Linear Elasticity on Anisotropic
Geometric Meshes . . . . . . . . . . . . ??
Manuel J. Castro and
Carlos Parés Well-Balanced High-Order Finite Volume
Methods for Systems of Balance Laws . . ??
Jiaxi Gu and
Jae-Hun Jung Adaptive Radial Basis Function Methods
for Initial Value Problems . . . . . . . ??
Ibrahim O. Sarumi and
Khaled M. Furati and
Abdul Q. M. Khaliq Highly Accurate Global Padé
Approximations of Generalized
Mittag-Leffler Function and Its Inverse ??
Levon Nurbekyan and
Alexander Iannantuono and
Adam M. Oberman No-Collision Transportation Maps . . . . ??
David P. Nicholls and
Carlos Pérez-Arancibia and
Catalin Turc Sweeping Preconditioners for the
Iterative Solution of Quasiperiodic
Helmholtz Transmission Problems in
Layered Media . . . . . . . . . . . . . ??
Lulu Tian and
Hui Guo and
Rui Jia and
Yang Yang An $h$-Adaptive Local Discontinuous
Galerkin Method for Simulating Wormhole
Propagation with Darcy--Forcheiner Model ??
Shuai Lou and
Chao Yan and
Li-Bin Ma and
Zhen-Hua Jiang The Flux Reconstruction Method with
Lax--Wendroff Type Temporal
Discretization for Hyperbolic
Conservation Laws . . . . . . . . . . . ??
David A. Craig Penner and
David W. Zingg Superconvergent Functional Estimates
from Tensor-Product Generalized
Summation-by-Parts Discretizations in
Curvilinear Coordinates . . . . . . . . ??
Arbaz Khan Spectral Method and Spectral Element
Method for Three Dimensional Linear
Elliptic System: Analysis and
Application . . . . . . . . . . . . . . ??
Wei Su and
Peng Wang and
Yonghao Zhang and
Lei Wu Implicit Discontinuous Galerkin Method
for the Boltzmann Equation . . . . . . . ??
Aytekin Cibik and
Fatma G. Eroglu and
Songül Kaya Analysis of Second Order Time Filtered
Backward Euler Method for MHD Equations ??
Thi-Thao-Phuong Hoang and
Lili Ju and
Zhu Wang Nonoverlapping Localized Exponential
Time Differencing Methods for Diffusion
Problems . . . . . . . . . . . . . . . . ??
Hao Li and
Xiangxiong Zhang Superconvergence of High Order Finite
Difference Schemes Based on Variational
Formulation for Elliptic Equations . . . ??
K. R. Arun and
S. Samantaray Asymptotic Preserving Low Mach Number
Accurate IMEX Finite Volume Schemes for
the Isentropic Euler Equations . . . . . ??
Xiaolong Zhang and
John P. Boyd Optimal Truncations for Multivariate
Fourier and Chebyshev Series: Mysteries
of the Hyperbolic Cross: Part I:
Bivariate Case . . . . . . . . . . . . . ??
Feng Chen and
Jie Shen Stability and Error Analysis of Operator
Splitting Methods for American Options
Under the Black--Scholes Model . . . . . ??
Guoqiao You and
Shingyu Leung Fast Construction of Forward Flow Maps
using Eulerian Based Interpolation
Schemes . . . . . . . . . . . . . . . . ??
Yanfang Yang and
Shubin Fu and
Eric T. Chung Online Mixed Multiscale Finite Element
Method with Oversampling and Its
Applications . . . . . . . . . . . . . . ??
Wenjuan Yao and
Jie Shen and
Zhichang Guo and
Jiebao Sun and
Boying Wu A Total Fractional-Order Variation Model
for Image Super-Resolution and Its SAV
Algorithm . . . . . . . . . . . . . . . ??
Isaac Harris Approximation of the Zero-Index
Transmission Eigenvalues with a
Conductive Boundary and Parameter
Estimation . . . . . . . . . . . . . . . ??
Hongxing Rui and
Yue Sun A MAC Scheme for Coupled Stokes--Darcy
Equations on Non-uniform Grids . . . . . ??
Rong Huang Accurate Eigenvalues of Some Generalized
Sign Regular Matrices via Relatively
Robust Representations . . . . . . . . . ??
Will Trojak and
Rob Watson and
Ashley Scillitoe and
Paul G. Tucker Effect of Mesh Quality on Flux
Reconstruction in Multi-dimensions . . . ??
Jan S. Hesthaven and
Fabian Mönkeberg Two-Dimensional RBF--ENO Method on
Unstructured Grids . . . . . . . . . . . ??
H. T. Huynh Discontinuous Galerkin via
Interpolation: The Direct Flux
Reconstruction Method . . . . . . . . . ??
Daniele Casati and
Ralf Hiptmair Coupling FEM with a Multiple-Subdomain
Trefftz Method . . . . . . . . . . . . . ??
James Kent A Positive Definite Limiter for
Advection Problems . . . . . . . . . . . ??
Benjamin W. Ong and
Satyen Dhamankar Towards an Adaptive Treecode for
$N$-body Problems . . . . . . . . . . . ??
Weifeng Zhao and
Wen-An Yong Boundary Scheme for a Discrete Kinetic
Approximation of the Navier--Stokes
Equations . . . . . . . . . . . . . . . ??
Siavosh Shadpey and
David W. Zingg Entropy-Stable Multidimensional
Summation-by-Parts Discretizations on
hp-Adaptive Curvilinear Grids for
Hyperbolic Conservation Laws . . . . . . ??
Gero Schnücke and
Nico Krais and
Thomas Bolemann and
Gregor J. Gassner Entropy Stable Discontinuous Galerkin
Schemes on Moving Meshes for Hyperbolic
Conservation Laws . . . . . . . . . . . ??
Enrico Facca and
Sara Daneri and
Franco Cardin and
Mario Putti Numerical Solution of Monge--Kantorovich
Equations via a Dynamic Formulation . . ??
Jiao-fen Li and
Wen Li and
Seak-Weng Vong and
Qi-Lun Luo and
MingQing Xiao A Riemannian Optimization Approach for
Solving the Generalized Eigenvalue
Problem for Nonsquare Matrix Pencils . . ??
Y. Rong and
J. A. Fiordilino Numerical Analysis of a BDF2 Modular
Grad--Div Stabilization Method for the
Navier--Stokes Equations . . . . . . . . ??
Juan A. Acebrón A Probabilistic Linear Solver Based on a
Multilevel Monte Carlo Method . . . . . ??
Tongke Wang and
Meng Qin and
Zhiyue Zhang The Puiseux Expansion and Numerical
Integration to Nonlinear Weakly Singular
Volterra Integral Equations of the
Second Kind . . . . . . . . . . . . . . ??
Youngsoo Ha and
Chang Ho Kim and
Hyoseon Yang and
Jungho Yoon Construction of an Improved Third-Order
WENO Scheme with a New Smoothness
Indicator . . . . . . . . . . . . . . . ??
Andrea A. Ruggiu and
Jan Nordström Multigrid Schemes for High Order
Discretizations of Hyperbolic Problems ??
François Bouchut and
Emmanuel Franck and
Laurent Navoret A Low Cost Semi-implicit Low-Mach
Relaxation Scheme for the Full Euler
Equations . . . . . . . . . . . . . . . ??
Xiaobing Feng and
Yukun Li and
Yi Zhang A Fully Discrete Mixed Finite Element
Method for the Stochastic Cahn--Hilliard
Equation with Gradient-Type
Multiplicative Noise . . . . . . . . . . ??
Difeng Cai and
Zhiqiang Cai and
Shun Zhang Robust Equilibrated Error Estimator for
Diffusion Problems: Mixed Finite
Elements in Two Dimensions . . . . . . . ??
Yiwei Feng and
Tiegang Liu and
Kun Wang A Characteristic-Featured Shock Wave
Indicator for Conservation Laws Based on
Training an Artificial Neuron . . . . . ??
Chaolong Jiang and
Yuezheng Gong and
Wenjun Cai and
Yushun Wang A Linearly Implicit
Structure--Preserving Scheme for the
Camassa--Holm Equation Based on Multiple
Scalar Auxiliary Variables Approach . . ??
Chunxiong Zheng and
Jiashun Hu Optimal Error Estimate of the
Extended--WKB Approximation to the High
Frequency Wave-Type Equation in the
Semi-classical Regime . . . . . . . . . ??
Paola Gervasio and
Luca Ded\`e and
Ondine Chanon and
Alfio Quarteroni A Computational Comparison Between
Isogeometric Analysis and Spectral
Element Methods: Accuracy and Spectral
Properties . . . . . . . . . . . . . . . ??
Xiaole Li and
Yulong Xing and
Ching-Shan Chou Optimal Energy Conserving and Energy
Dissipative Local Discontinuous Galerkin
Methods for the Benjamin--Bona--Mahony
Equation . . . . . . . . . . . . . . . . ??
Liu Fengnan and
Yasuhide Fukumoto and
Xiaopeng Zhao A Linearized Finite Difference Scheme
for the Richards Equation Under
Variable-Flux Boundary Conditions . . . ??
Geonwoo Kim and
Junghee Cho and
Myungjoo Kang Cauchy Noise Removal by Weighted Nuclear
Norm Minimization . . . . . . . . . . . ??
Weina Wang and
Chunlin Wu and
Xue-Cheng Tai A Globally Convergent Algorithm for a
Constrained Non--Lipschitz Image
Restoration Model . . . . . . . . . . . ??
Lidia Aceto and
Paolo Novati Padé-type Approximations to the Resolvent
of Fractional Powers of Operators . . . ??
Mahdi Hassanzadeh and
Mahmood Mazare Computation of Design Sensitivities in
Steady-State Incompressible Laminar
Flows Based on New Semi-Analytical
Method . . . . . . . . . . . . . . . . . ??
Haiyan Su and
Xinlong Feng and
Jianping Zhao On Two-Level Oseen Penalty Iteration
Methods for the $2$D/$3$D Stationary
Incompressible Magnetohydronamics . . . ??
Yong-Liang Zhao and
Pei-Yong Zhu and
Xian-Ming Gu and
Xi-Le Zhao and
Huan-Yan Jian A Preconditioning Technique for
All-at-Once System from the Nonlinear
Tempered Fractional Diffusion Equation ??
Minghui Liu and
Boying Wu and
Xiong Meng Optimal Error Estimates of the
Discontinuous Galerkin Method with
Upwind-Biased Fluxes for $2$D Linear
Variable Coefficients Hyperbolic
Equations . . . . . . . . . . . . . . . ??
Matteo Cicuttin and
Alexandre Ern and
Thirupathi Gudi Hybrid High-Order Methods for the
Elliptic Obstacle Problem . . . . . . . ??
Jun Zhu and
Feng Zheng and
Jianxian Qiu New Finite Difference Hermite WENO
Schemes for Hamilton--Jacobi Equations ??
M. Semplice and
G. Visconti Efficient Implementation of Adaptive
Order Reconstructions . . . . . . . . . ??
Vít Dolejsí and
Petr Tichý On Efficient Numerical Solution of
Linear Algebraic Systems Arising in
Goal-Oriented Error Estimates . . . . . ??
Lai Wang and
Meilin Yu Comparison of ROW, ESDIRK, and BDF2 for
Unsteady Flows with the High-Order Flux
Reconstruction Formulation . . . . . . . ??
Jinye Shen and
Changpin Li and
Zhi-zhong Sun An H2N2 Interpolation for Caputo
Derivative with Order in (1, 2) and Its
Application to Time-Fractional Wave
Equations in More Than One Space
Dimension . . . . . . . . . . . . . . . ??
Milad Karimi and
Fridoun Moradlou and
Mojtaba Hajipour Regularization Technique for an Inverse
Space-Fractional Backward Heat
Conduction Problem . . . . . . . . . . . ??
Arthur Bousquet and
Youngjoon Hong and
Roger Temam and
Joseph Tribbia Numerical Simulations of the
Two-Dimensional Inviscid Hydrostatic
Primitive Equations with Humidity and
Saturation . . . . . . . . . . . . . . . ??
Tsung-Ming Huang and
Tiexiang Li and
Jia-Wei Lin and
Wen-Wei Lin and
Heng Tian Structure-Preserving Methods for
Computing Complex Band Structures of
Three Dimensional Photonic Crystals . . ??
Myeong-Hwan Ahn and
Duck-Joo Lee Modified Monotonicity Preserving
Constraints for High-Resolution
Optimized Compact Scheme . . . . . . . . ??
Daxin Nie and
Jing Sun and
Weihua Deng Numerical Scheme for the Fokker--Planck
Equations Describing Anomalous
Diffusions with Two Internal States . . ??
Wei Zhu Image Denoising Using $ L^p$-norm of
Mean Curvature of Image Surface . . . . ??
Chao Zhang and
Igor Menshov Eulerian Model for Simulating
Multi-Fluid Flows with an Arbitrary
Number of Immiscible Compressible
Components . . . . . . . . . . . . . . . ??
H. Hassani and
J. A. Tenreiro Machado and
Z. Avazzadeh and
E. Naraghirad and
M. Sh. Dahaghin Generalized Bernoulli Polynomials:
Solving Nonlinear $2$D Fractional
Optimal Control Problems . . . . . . . . ??
Saihua Wang and
Feng Wang and
Xuejun Xu A Rigorous Condition Number Estimate of
an Immersed Finite Element Method . . . ??
Qilong Guo and
Dong Sun and
Chen Li and
Pengxin Liu and
Hanxin Zhang A New Discontinuity Indicator for Hybrid
WENO Schemes . . . . . . . . . . . . . . ??
Matteo Ioriatti and
Michael Dumbser and
Raphaël Loub\`ere A Staggered Semi-implicit Discontinuous
Galerkin Scheme with a Posteriori
Subcell Finite Volume Limiter for the
Euler Equations of Gasdynamics . . . . . ??
Tiankui Zhang and
Charles W. Wolgemuth Sixth-Order Accurate Schemes for
Reinitialization and Extrapolation in
the Level Set Framework . . . . . . . . ??
Wentao Cai and
Jilu Wang and
Kai Wang Convergence Analysis of Crank--Nicolson
Galerkin--Galerkin FEMs for Miscible
Displacement in Porous Media . . . . . . ??
Yu Du and
Haijun Wu A Pure Source Transfer Domain
Decomposition Method for Helmholtz
Equations in Unbounded Domain . . . . . ??
Yingxia Xi and
Xia Ji and
Shuo Zhang A High Accuracy Nonconforming Finite
Element Scheme for Helmholtz
Transmission Eigenvalue Problem . . . . ??
Xiao Wen and
Wai Sun Don and
Zhen Gao and
Yulong Xing Entropy Stable and Well-Balanced
Discontinuous Galerkin Methods for the
Nonlinear Shallow Water Equations . . . ??
Dongfang Li and
Weiwei Sun Linearly Implicit and High-Order
Energy-Conserving Schemes for Nonlinear
Wave Equations . . . . . . . . . . . . . ??
Di Qiu and
Lok Ming Lui Inconsistent Surface Registration via
Optimization of Mapping Distortions . . ??
Carlos A. Pereira and
Brian C. Vermeire Fully-Discrete Analysis of High-Order
Spatial Discretizations with Optimal
Explicit Runge--Kutta Methods . . . . . ??
C. Escalante and
T. Morales de Luna A General Non-hydrostatic Hyperbolic
Formulation for Boussinesq Dispersive
Shallow Flows and Its Numerical
Approximation . . . . . . . . . . . . . ??
Geraldine Tour and
Nawdha Thakoor and
Jingtang Ma and
Désiré Yannick Tangman A Spectral Element Method for Option
Pricing Under Regime-Switching with
Jumps . . . . . . . . . . . . . . . . . ??
Benjamin W. Ong and
Raymond J. Spiteri Deferred Correction Methods for Ordinary
Differential Equations . . . . . . . . . ??
Lu Zhang and
Qifeng Zhang and
Hai-Wei Sun Exponential Runge--Kutta Method for
Two-Dimensional Nonlinear Fractional
Complex Ginzburg--Landau Equations . . . ??
Joscha Gedicke and
Sjoerd Geevers and
Ilaria Perugia An Equilibrated a Posteriori Error
Estimator for Arbitrary-Order Nédélec
Elements for Magnetostatic Problems . . ??
Zhen Xu and
Xiaofeng Yang and
Hui Zhang Error Analysis of a Decoupled, Linear
Stabilization Scheme for the
Cahn--Hilliard Model of Two-Phase
Incompressible Flows . . . . . . . . . . ??
Giovanni Di Ilio and
Stefano Ubertini and
Sauro Succi and
Giacomo Falcucci Nanofluid Heat Transfer in Wavy-Wall
Channels with Different Geometries: a
Finite-Volume Lattice Boltzmann Study ??
Maria Strazzullo and
Francesco Ballarin and
Gianluigi Rozza POD--Galerkin Model Order Reduction for
Parametrized Time Dependent Linear
Quadratic Optimal Control Problems in
Saddle Point Formulation . . . . . . . . ??
Yupeng Ren and
Tao Xiong and
Jianxian Qiu A Hybrid Finite Difference WENO--ZQ Fast
Sweeping Method for Static
Hamilton--Jacobi Equations . . . . . . . ??
Maolin Che and
Yimin Wei Multiplicative Algorithms for Symmetric
Nonnegative Tensor Factorizations and
Its Applications . . . . . . . . . . . . ??
Yanling Deng and
Fei Wang and
Huayi Wei A Posteriori Error Estimates of Virtual
Element Method for a Simplified Friction
Problem . . . . . . . . . . . . . . . . ??
Samir Karaa and
Amiya K. Pani Mixed FEM for Time-Fractional Diffusion
Problems with Time-Dependent
Coefficients . . . . . . . . . . . . . . ??
Shouwen Sun and
Jun Li and
Jia Zhao and
Qi Wang Structure-Preserving Numerical
Approximations to a Non-isothermal
Hydrodynamic Model of Binary Fluid Flows ??
Xiao Wen and
Wai Sun Don and
Zhen Gao and
Jan S. Hesthaven An Edge Detector Based on Artificial
Neural Network with Application to
Hybrid Compact--WENO Finite Difference
Scheme . . . . . . . . . . . . . . . . . ??
Hana Mizerová and
Bangwei She Convergence and Error Estimates for a
Finite Difference Scheme for the
Multi-dimensional Compressible
Navier--Stokes System . . . . . . . . . ??
Martin J. Gander and
Pratik M. Kumbhar and
Albert E. Ruehli Asymptotic Analysis for Overlap in
Waveform Relaxation Methods for RC Type
Circuits . . . . . . . . . . . . . . . . ??
Yuan Xu and
Xiong Meng and
Chi-Wang Shu and
Qiang Zhang Superconvergence Analysis of the
Runge--Kutta Discontinuous Galerkin
Methods for a Linear Hyperbolic Equation ??
Yihui Han and
Huangxin Chen and
Xiao-Ping Wang and
Xiaoping Xie EXtended HDG Methods for Second Order
Elliptic Interface Problems . . . . . . ??
Xing Liu and
Weihua Deng Numerical Approximation for Fractional
Diffusion Equation Forced by a Tempered
Fractional Gaussian Noise . . . . . . . ??
Jeonghun J. Lee A Mixed Method for Time-Transient
Acoustic Wave Propagation in
Metamaterials . . . . . . . . . . . . . ??
L.-B. Maier Sparse Data Interpolation and Smoothing
on Embedded Submanifolds . . . . . . . . ??
El Hassan Ben-Ahmed and
Mohamed Sadik and
Mohamed Wakrim A Stable Radial Basis Function Partition
of Unity Method with $d$ -Rectangular
Patches for Modelling Water Flow in
Porous Media . . . . . . . . . . . . . . ??
Hendrik Ranocha and
David I. Ketcheson Relaxation Runge--Kutta Methods for
Hamiltonian Problems . . . . . . . . . . ??
Ya-Nan Zhu and
Xiaoqun Zhang Stochastic Primal Dual Fixed Point
Method for Composite Optimization . . . ??
Changli Liu and
Jungong Xue and
Ren-Cang Li Accurate Numerical Solution for Shifted
$M$-Matrix Algebraic Riccati Equations ??
Yingzhi Liu and
Yinnian He Two-Level Schwarz Methods for a
Discontinuous Galerkin Approximation of
Elliptic Problems with Jump Coefficients ??
Wansheng Wang and
Lijun Yi and
Aiguo Xiao A Posteriori Error Estimates for Fully
Discrete Finite Element Method for
Generalized Diffusion Equation with
Delay . . . . . . . . . . . . . . . . . ??
Hui Liang and
Hermann Brunner The Fine Error Estimation of Collocation
Methods on Uniform Meshes for Weakly
Singular Volterra Integral Equations . . ??
Chongyang Deng and
Xiali Fan and
Ming-Jun Lai A Minimization Approach for Constructing
Generalized Barycentric Coordinates and
Its Computation . . . . . . . . . . . . ??
Zhong-qi Kyle Tian and
Jennifer Crodelle and
Douglas Zhou A Combined Offline--Online Algorithm for
Hodgkin--Huxley Neural Networks . . . . ??
Andreas Rupp and
Sanghyun Lee Continuous Galerkin and Enriched
Galerkin Methods with Arbitrary Order
Discontinuous Trial Functions for the
Elliptic and Parabolic Problems with
Jump Conditions . . . . . . . . . . . . ??
Rongjun Cao and
Minghua Chen and
Michael K. Ng and
Yu-Jiang Wu Fast and High-Order Accuracy Numerical
Methods for Time-Dependent Nonlocal
Problems in $ {\mathbb {R}}^2 $ . . . . ??
Gung-Min Gie and
Chang-Yeol Jung and
Hoyeon Lee Enriched Finite Volume Approximations of
the Plane--Parallel Flow at a Small
Viscosity . . . . . . . . . . . . . . . ??
Jing Sun and
Daxin Nie and
Weihua Deng Error Estimates for Backward Fractional
Feynman--Kac Equation with Non-Smooth
Initial Data . . . . . . . . . . . . . . ??
Shun Zhang Robust and Local Optimal A Priori Error
Estimates for Interface Problems with
Low Regularity: Mixed Finite Element
Approximations . . . . . . . . . . . . . ??
Praveen Chandrashekar and
Rakesh Kumar Constraint Preserving Discontinuous
Galerkin Method for Ideal Compressible
MHD on $2$-D Cartesian Grids . . . . . . ??
Jincheng Ren and
Hong-lin Liao and
Zhimin Zhang Superconvergence Error Estimate of a
Finite Element Method on Nonuniform Time
Meshes for Reaction--Subdiffusion
Equations . . . . . . . . . . . . . . . ??
Gang Wang and
Ying Wang and
Yinnian He A Posteriori Error Estimates for the
Virtual Element Method for the Stokes
Problem . . . . . . . . . . . . . . . . ??
Wen-An Yong and
Weifeng Zhao Numerical Analysis of the Lattice
Boltzmann Method for the Boussinesq
Equations . . . . . . . . . . . . . . . ??
Slimane Adjerid and
Tao Lin and
Qiao Zhuang Error Estimates for an Immersed Finite
Element Method for Second Order
Hyperbolic Equations in Inhomogeneous
Media . . . . . . . . . . . . . . . . . ??
Dongho Kim and
Eun-Jae Park and
Boyoon Seo Convergence of Multi-level Algorithms
for a Class of Nonlinear Problems . . . ??
Xiang Xu and
Yanxiang Zhao Maximum Principle Preserving Schemes for
Binary Systems with Long--Range
Interactions . . . . . . . . . . . . . . ??
Guangnan Huang and
Songting Luo Hybrid Fast Sweeping Methods for
Anisotropic Eikonal Equation in
Two-Dimensional Tilted Transversely
Isotropic Media . . . . . . . . . . . . ??
Alexandre Bourriaud and
Raphaël Loub\`ere and
Rodolphe Turpault A Priori Neural Networks Versus A
Posteriori MOOD Loop: a High Accurate
$1$D FV Scheme Testing Bed . . . . . . . ??
Piotr Minakowski and
Thomas Richter Finite Element Error Estimates on
Geometrically Perturbed Domains . . . . ??
Wanderson Lambert and
Amaury Alvarez and
Ismael Ledoino and
Duilio Tadeu and
Dan Marchesin and
Johannes Bruining Mathematics and Numerics for Balance
Partial Differential--Algebraic
Equations (PDAEs) . . . . . . . . . . . ??
Jad Dabaghi and
Vincent Martin and
Martin Vohralík Adaptive Inexact Semismooth Newton
Methods for the Contact Problem Between
Two Membranes . . . . . . . . . . . . . ??
Wenbin Chen and
Cheng Wang and
Shufen Wang and
Xiaoming Wang and
Steven M. Wise Energy Stable Numerical Schemes for
Ternary Cahn--Hilliard System . . . . . ??
Qinjie Liu and
Shun Zhang Adaptive Flux--Only Least--Squares
Finite Element Methods for Linear
Transport Equations . . . . . . . . . . ??
Lexing Ying Mirror Descent Algorithms for Minimizing
Interacting Free Energy . . . . . . . . ??
Jun Yang The Iterative Methods for Solving
Pseudomontone Equilibrium Problems . . . ??
Ping-Fan Dai A Fixed Point Iterative Method for
Tensor Complementarity Problems . . . . ??
Jianying Zhang Stability of Linear Multistep Time
Iterations with the WENO5 Discretization
at Discontinuities . . . . . . . . . . . ??
Xiaoying Dai and
Xiong Kuang and
Jack Xin and
Aihui Zhou Two-Grid Based Adaptive Proper
Orthogonal Decomposition Method for Time
Dependent Partial Differential Equations ??
M. Huska and
D. Lazzaro and
S. Morigi and
A. Samor\`e and
G. Scrivanti Spatially-Adaptive Variational
Reconstructions for Linear Inverse
Electrical Impedance Tomography . . . . ??
Sudeep Kundu and
Amiya Kumar Pani Global Stabilization of Two Dimensional
Viscous Burgers' Equation by Nonlinear
Neumann Boundary Feedback Control and
Its Finite Element Analysis . . . . . . ??
Hong Zhang and
Zhengyu Liu and
Emil Constantinescu and
Robert Jacob Stability Analysis of Interface
Conditions for Ocean--Atmosphere
Coupling . . . . . . . . . . . . . . . . ??
Lindsay Martin and
Yen-Hsi Richard Tsai Equivalent Extensions of
Hamilton--Jacobi-Bellman Equations on
Hypersurfaces . . . . . . . . . . . . . ??
Viktor Reshniak and
Yuri Melnikov Method of Green's Potentials for
Elliptic PDEs in Domains with Random
Apertures . . . . . . . . . . . . . . . ??
Ching-Sung Liu A Positivity Preserving Iterative Method
for Finding the Ground States of
Saturable Nonlinear Schrödinger Equations ??
Zhangpeng Sun and
Wenqi Yao and
Tiao Lu Optimization Modeling and Simulating of
the Stationary Wigner Inflow Boundary
Value Problem . . . . . . . . . . . . . ??
Stefan Langer and
R. C. Swanson On Boundary-Value Problems for RANS
Equations and Two-Equation Turbulence
Models . . . . . . . . . . . . . . . . . ??
Huan Liu and
Aijie Cheng and
Hong Wang A Parareal Finite Volume Method for
Variable--Order Time-Fractional
Diffusion Equations . . . . . . . . . . ??
Xue Chen and
Zhong-bao Wang and
Zhang-you Chen A New Method for Solving Variational
Inequalities and Fixed Points Problems
of Demi--Contractive Mappings in Hilbert
Spaces . . . . . . . . . . . . . . . . . ??
Yao Jin and
Fei Liao and
Jinsheng Cai Compact Schemes for Multiscale Flows
with Cell--Centered Finite Difference
Method . . . . . . . . . . . . . . . . . ??
Jun Guo and
Minfu Feng A New Projection--Based Stabilized
Virtual Element Method for the Stokes
Problem . . . . . . . . . . . . . . . . ??
Shimin Guo and
Liquan Mei and
Can Li and
Zhengqiang Zhang and
Ying Li Semi-implicit Hermite--Galerkin Spectral
Method for Distributed--Order
Fractional-in-Space Nonlinear
Reaction--Diffusion Equations in
Multidimensional Unbounded Domains . . . ??
Ricardo Oyarzúa and
Miguel Serón A Divergence-Conforming DG-Mixed Finite
Element Method for the Stationary
Boussinesq Problem . . . . . . . . . . . ??
Juntao Huang and
Yuan Liu and
Wei Guo and
Zhanjing Tao and
Yingda Cheng An Adaptive Multiresolution Interior
Penalty Discontinuous Galerkin Method
for Wave Equations in Second Order Form ??
Jian Cheng and
Fan Zhang and
Tiegang Liu A Quasi-Conservative Discontinuous
Galerkin Method for Solving Five
Equation Model of Compressible
Two-Medium Flows . . . . . . . . . . . . ??
Ilham Asmouh and
Mofdi El-Amrani and
Mohammed Seaid and
Naji Yebari A Conservative Semi-Lagrangian Finite
Volume Method for Convection--Diffusion
Problems on Unstructured Grids . . . . . ??
A. Caiazzo and
R. Maier and
D. Peterseim Reconstruction of Quasi-Local Numerical
Effective Models from Low-Resolution
Measurements . . . . . . . . . . . . . . ??
Rihui Lan and
Pengtao Sun A Novel Arbitrary Lagrangian--Eulerian
Finite Element Method for a Mixed
Parabolic Problem in a Moving Domain . . ??
Shukai Du HDG Methods for Stokes Equation Based on
Strong Symmetric Stress Formulations . . ??
Haixiang Zhang and
Xuehua Yang and
Da Xu An Efficient Spline Collocation Method
for a Nonlinear Fourth-Order Reaction
Subdiffusion Equation . . . . . . . . . ??
Tobias Linn and
Kai Bittner and
Hans Georg Brachtendorf and
Christoph Jungemann Simulation of THz Oscillations in
Semiconductor Devices Based on Balance
Equations . . . . . . . . . . . . . . . ??
Erwan Deriaz and
Pierre Haldenwang Non-linear CFL Conditions Issued from
the von Neumann Stability Analysis for
the Transport Equation . . . . . . . . . ??
M. Benzakour Amine Linearized Implicit Methods Based on a
Single--Layer Neural Network:
Application to Keller--Segel Models . . ??
Guohui Song and
Gabe Tucker and
Congzhi Xia Admissible Concentration Factors for
Edge Detection from Non-uniform Fourier
Data . . . . . . . . . . . . . . . . . . ??
Jin Zhang and
Xiaowei Liu Optimal Order of Uniform Convergence for
Finite Element Method on Bakhvalov-Type
Meshes . . . . . . . . . . . . . . . . . ??
Stephen D. Farnham and
Lixin Shen and
Bruce W. Suter Principal Component Projection with
Low-Degree Polynomials . . . . . . . . . ??
Richard Archibald and
Feng Bao and
Jiongmin Yong and
Tao Zhou An Efficient Numerical Algorithm for
Solving Data Driven Feedback Control
Problems . . . . . . . . . . . . . . . . ??
Jordi Feliu-Fab\`a and
Lexing Ying Hierarchical Interpolative Factorization
Preconditioner for Parabolic Equations ??
Raimund Bürger and
Enrique D. Fernández-Nieto and
Víctor Osores A Multilayer Shallow Water Approach for
Polydisperse 40Sedimentation with
Sediment Compressibility and Mixture
Viscosity . . . . . . . . . . . . . . . ??
Carlos A. Pereira and
Brian C. Vermeire Spectral Properties of High-Order
Element Types for Implicit Large Eddy
Simulation . . . . . . . . . . . . . . . ??
Hailong Qiu Error Analysis of Euler Semi-implicit
Scheme for the Nonstationary
Magneto-hydrodynamics Problem with
Temperature Dependent Parameters . . . . ??
Xueying Zhao and
Minru Bai and
Michael K. Ng Nonconvex Optimization for Robust Tensor
Completion from Grossly Sparse
Observations . . . . . . . . . . . . . . ??
Wenbin Chen and
Daozhi Han and
Xiaoming Wang and
Yichao Zhang Uniquely Solvable and Energy Stable
Decoupled Numerical Schemes for the
Cahn--Hilliard--Navier--Stokes--Darcy--Boussinesq System ??
Sergio Caucao and
Gabriel N. Gatica and
Ricardo Oyarzúa and
Nestor Sánchez A Fully--Mixed Formulation for the
Steady Double--Diffusive Convection
System Based upon Brinkman--Forchheimer
Equations . . . . . . . . . . . . . . . ??
R. Abgrall and
J. Nordström and
P. Öffner and
S. Tokareva Analysis of the SBP--SAT Stabilization
for Finite Element Methods. Part I:
Linear Problems . . . . . . . . . . . . ??
Qiang Du and
Jiang Yang and
Zhi Zhou Time-Fractional Allen--Cahn Equations:
Analysis and Numerical Methods . . . . . ??
Changpin Li and
Zhiqiang Li and
Zhen Wang Mathematical Analysis and the Local
Discontinuous Galerkin Method for
Caputo--Hadamard Fractional Partial
Differential Equation . . . . . . . . . ??
Dimitri Breda and
Toshikazu Kuniya and
Jordi Ripoll and
Rossana Vermiglio Collocation of Next-Generation Operators
for Computing the Basic Reproduction
Number of Structured Populations . . . . ??
Boya Zhou and
Xiaoli Chen and
Dongfang Li Nonuniform Alikhanov Linearized Galerkin
Finite Element Methods for Nonlinear
Time-Fractional Parabolic Equations . . ??
Hamed Jalali Khouzani and
Ramin Kamali Moghadam A Novel Approach of Unsteady Adjoint
Lattice Boltzmann Method Based on
Circular Function Scheme . . . . . . . . ??
Huan Pan and
You-Wei Wen and
Tieyong Zeng Constrained Total Variation Based
Three-Dimension Single Particle
Reconstruction in Cryogenic Electron
Microscopy . . . . . . . . . . . . . . . ??
Hayley Guy and
Alen Alexanderian and
Meilin Yu A Distributed Active Subspace Method for
Scalable Surrogate Modeling of Function
Valued Outputs . . . . . . . . . . . . . ??
Guangzhi Du and
Liyun Zuo A Parallel Iterative Finite Element
Method for the Linear Elliptic Equations ??
Peng Zhu and
Shenglan Xie A Uniformly Convergent Weak Galerkin
Finite Element Method on Shishkin Mesh
for $1$ d Convection--Diffusion Problem ??
Radu Ioan Bot and
Axel Böhm Variable Smoothing for Convex
Optimization Problems Using Stochastic
Gradients . . . . . . . . . . . . . . . ??
Giselle Sosa Jones and
Jeonghun J. Lee and
Sander Rhebergen A Space--Time Hybridizable Discontinuous
Galerkin Method for Linear Free-Surface
Waves . . . . . . . . . . . . . . . . . ??
Xin Liu A Well-Balanced and
Positivity-Preserving Numerical Model
for Shallow Water Flows in Channels with
Wet--Dry Fronts . . . . . . . . . . . . ??
Binjie Li and
Tao Wang and
Xiaoping Xie Numerical Analysis of Two Galerkin
Discretizations with Graded Temporal
Grids for Fractional Evolution Equations ??
Hailong Qiu Well-Posedness and Finite Element
Approximation for the Stationary
Magneto-Hydrodynamics Problem with
Temperature-Dependent Parameters . . . . ??
Chungen Shen and
Wenjuan Xue and
Lei-Hong Zhang and
Baiyun Wang An Active-Set Proximal-Newton Algorithm
for $ \ell_1 $ Regularized Optimization
Problems with Box Constraints . . . . . ??
Min Ling and
Fei Wang and
Weimin Han The Nonconforming Virtual Element Method
for a Stationary Stokes Hemivariational
Inequality with Slip Boundary Condition ??
Jingtang Ma and
Jianjun Ma Finite Difference Methods for the
Hamilton--Jacobi-Bellman Equations
Arising in Regime Switching Utility
Maximization . . . . . . . . . . . . . . ??
Bochra Djeridi and
Radouen Ghanem and
Hocine Sissaoui Spectral Element Methods a Priori and a
Posteriori Error Estimates for Penalized
Unilateral Obstacle Problem . . . . . . ??
Cun-Qiang Miao On Chebyshev--Davidson Method for
Symmetric Generalized Eigenvalue
Problems . . . . . . . . . . . . . . . . ??
Yingying Xie and
Liuqiang Zhong Convergence of Adaptive Weak Galerkin
Finite Element Methods for Second Order
Elliptic Problems . . . . . . . . . . . ??
Yan Jiang High Order Finite Difference
Multi-resolution WENO Method for
Nonlinear Degenerate Parabolic Equations ??
H. Carrillo and
C. Parés and
D. Zorío Lax--Wendroff Approximate Taylor Methods
with Fast and Optimized Weighted
Essentially Non-oscillatory
Reconstructions . . . . . . . . . . . . ??
E. Abreu and
V. Matos and
J. Pérez and
P. Rodríguez-Bermúdez A Class of Lagrangian--Eulerian
Shock--Capturing Schemes for First-Order
Hyperbolic Problems with Forcing Terms ??
B. Kheirfam and
A. Nasrollahi and
M. Mohammadi A Second-Order Corrector Infeasible
Interior--Point Method for Semidefinite
Optimization Based on a Wide
Neighborhood . . . . . . . . . . . . . . ??
A. Taiwo and
L. O. Jolaoso and
O. T. Mewomo Inertial-Type Algorithm for Solving
Split Common Fixed Point Problems in
Banach Spaces . . . . . . . . . . . . . ??
Kwunlun Chu and
Shingyu Leung A Level Set Method for the Dirichlet $k$
-Partition Problem . . . . . . . . . . . ??
Joackim Bernier and
Nicolas Crouseilles and
Yingzhe Li Exact Splitting Methods for Kinetic and
Schrödinger Equations . . . . . . . . . . ??
Azita Tajaddini and
Gang Wu and
Farid Saberi-Movahed and
Najmeh Azizizadeh Two New Variants of the Simpler Block
GMRES Method with Vector Deflation and
Eigenvalue Deflation for Multiple Linear
Systems . . . . . . . . . . . . . . . . ??
Shuying Zhai and
Zhifeng Weng and
Xinlong Feng and
Yinnian He Stability and Error Estimate of the
Operator Splitting Method for the Phase
Field Crystal Equation . . . . . . . . . ??
Hongsong Feng and
Guangqing Long and
Shan Zhao FFT-Based High Order Central Difference
Schemes for Poisson's Equation with
Staggered Boundaries . . . . . . . . . . ??
Chiu-Yen Kao and
Seyyed Abbas Mohammadi and
Braxton Osting Linear Convergence of a Rearrangement
Method for the One-dimensional Poisson
Equation . . . . . . . . . . . . . . . . ??
Jinqiang Chen and
Peixiang Yu and
Hua Ouyang and
Zhen F. Tian A Novel Parallel Computing Strategy for
Compact Difference Schemes with
Consistent Accuracy and Dispersion . . . ??
Chao Zhang and
Yan Xu and
Yinhua Xia Local Discontinuous Galerkin Methods to
a Dispersive System of KdV-Type
Equations . . . . . . . . . . . . . . . ??
Wasilij Barsukow The Active Flux Scheme for Nonlinear
Problems . . . . . . . . . . . . . . . . ??
Paola F. Antonietti and
Jacopo De Ponti and
Luca Formaggia and
Anna Scotti Preconditioning Techniques for the
Numerical Solution of Flow in Fractured
Porous Media . . . . . . . . . . . . . . ??
Andrew J. Christlieb and
Pierson T. Guthrey and
William A. Sands and
Mathialakan Thavappiragasm Parallel Algorithms for Successive
Convolution . . . . . . . . . . . . . . ??
Xin Chen and
Martin J. Gander and
Yingxiang Xu Optimized Schwarz Methods with
Elliptical Domain Decompositions . . . . ??
Lexing Ying Natural Gradient for Combined Loss Using
Wavelets . . . . . . . . . . . . . . . . ??
J. Garres-Díaz and
E. D. Fernández-Nieto and
A. Mangeney and
T. Morales de Luna A Weakly Non-hydrostatic Shallow Model
for Dry Granular Flows . . . . . . . . . ??
Yirang Yuan and
Changfeng Li and
Qing Yang Mixed Finite Element--Second Order
Upwind Fractional Step Difference Scheme
of Darcy--Forchheimer Miscible
Displacement and Its Numerical Analysis ??
Ibrahim O. Sarumi and
Khaled M. Furati and
Abdul Q. M. Khaliq and
Kassem Mustapha Generalized Exponential Time
Differencing Schemes for Stiff
Fractional Systems with Nonsmooth Source
Term . . . . . . . . . . . . . . . . . . ??
Kim-Ngan Le and
Martin Stynes An $ \alpha $-Robust Semidiscrete Finite
Element Method for a Fokker--Planck
Initial-Boundary Value Problem with
Variable-Order Fractional Time
Derivative . . . . . . . . . . . . . . . ??
Yanli Liu and
Yunbei Xu and
Wotao Yin Acceleration of Primal--Dual Methods by
Preconditioning and Simple Subproblem
Procedures . . . . . . . . . . . . . . . ??
Bo Wang and
Zhiguo Yang and
Li-Lian Wang and
Shidong Jiang On Time-Domain NRBC for Maxwell's
Equations and Its Application in
Accurate Simulation of Electromagnetic
Invisibility Cloaks . . . . . . . . . . ??
Hongyan Liu and
Changtao Sheng and
Li-Lian Wang and
Huifang Yuan On Diagonal Dominance of FEM Stiffness
Matrix of Fractional Laplacian and
Maximum Principle Preserving Schemes for
the Fractional Allen--Cahn Equation . . ??
Mohammadreza Yarmohammadi and
Shahnam Javadi Piecewise Fractional Interpolation with
Application to Fractional Differential
Equation . . . . . . . . . . . . . . . . ??
Tomas Lundquist and
Jan Nordström and
Arnaud Malan Stable Dynamical Adaptive Mesh
Refinement . . . . . . . . . . . . . . . ??
Jeffery M. Allen and
Justin Chang and
FrançoisL. E. Usseglio-Viretta and
Peter Graf and
Kandler Smith A Segregated Approach for Modeling the
Electrochemistry in the $3$-D
Microstructure of Li-Ion Batteries and
Its Acceleration Using Block
Preconditioners . . . . . . . . . . . . ??
Gary P. T. Choi and
Chris H. Rycroft Volumetric Density-Equalizing Reference
Map with Applications . . . . . . . . . ??
Chiu-Yen Kao and
Seyyed Abbas Mohammadi Extremal Rearrangement Problems
Involving Poisson's Equation with Robin
Boundary Conditions . . . . . . . . . . ??
Guosheng Fu and
Christoph Lehrenfeld and
Alexander Linke and
Timo Streckenbach Locking-Free and Gradient-Robust $ \vec
{H} $(div)-Conforming HDG Methods for
Linear Elasticity . . . . . . . . . . . ??
Yue Xie and
Stephen J. Wright Complexity of Proximal Augmented
Lagrangian for Nonconvex Optimization
with Nonlinear Equality Constraints . . ??
Elena Gaburro and
Michael Dumbser A Posteriori Subcell Finite Volume
Limiter for General $ P_N P_M $ Schemes:
Applications from Gasdynamics to
Relativistic Magnetohydrodynamics . . . ??
Jason E. Hicken On Entropy-Stable Discretizations and
the Entropy Adjoint . . . . . . . . . . ??
Yunqing Huang and
Meng Chen and
Jichun Li Developing and Analyzing New
Unconditionally Stable Finite Element
Schemes for Maxwell's Equations in
Complex Media . . . . . . . . . . . . . ??
Meng Cai and
Siqing Gan and
Xiaojie Wang Weak Convergence Rates for an Explicit
Full-Discretization of Stochastic
Allen--Cahn Equation with Additive Noise ??
Vladislav Balashov and
Alexander Zlotnik On a New Spatial Discretization for a
Regularized $3$D Compressible Isothermal
Navier--Stokes--Cahn--Hilliard System of
Equations with Boundary Conditions . . . ??
Xinyu Cheng and
Dong Li and
Keith Promislow and
Brian Wetton Asymptotic Behaviour of Time Stepping
Methods for Phase Field Models . . . . . ??
Zi-Hang She and
Cheng-Xue Lao and
Hong Yang and
Fu-Rong Lin Banded Preconditioners for Riesz Space
Fractional Diffusion Equations . . . . . ??
Stefan C. Schonsheck and
Michael M. Bronstein and
Rongjie Lai Nonisometric Surface Registration via
Conformal Laplace--Beltrami Basis
Pursuit . . . . . . . . . . . . . . . . ??
Xiangcheng Zheng and
V. J. Ervin and
Hong Wang Optimal Petrov--Galerkin Spectral
Approximation Method for the Fractional
Diffusion, Advection, Reaction Equation
on a Bounded Interval . . . . . . . . . ??
Diego Álvarez and
Pedro González-Rodríguez and
Manuel Kindelan A Local Radial Basis Function Method for
the Laplace--Beltrami Operator . . . . . ??
Xiaobin Liu and
Dazhi Zhang and
Xiong Meng and
Boying Wu Superconvergence of the Local
Discontinuous Galerkin Method for One
Dimensional Nonlinear
Convection--Diffusion Equations . . . . ??
Dong Wang An Efficient Iterative Method for
Reconstructing Surface from Point Clouds ??
Haitao Leng Adaptive HDG Methods for the
Steady-State Incompressible
Navier--Stokes Equations . . . . . . . . ??
Nicole Beisiegel and
Cristóbal E. Castro and
Jörn Behrens Metrics for Performance Quantification
of Adaptive Mesh Refinement . . . . . . ??
Tingting Hao and
Xiaofei Guan and
Shipeng Mao and
Shaochun Chen Computable Interpolation Error Constants
for the Geometric Simplex Finite
Elements . . . . . . . . . . . . . . . . ??
Chenhui Zhang and
Jie Ouyang and
Xiaodong Wang and
Yong Chai and
Mengxia Ma Analysis of the Energy Stability for
Stabilized Semi-implicit Schemes of the
Functionalized Cahn--Hilliard
Mass-conserving Gradient Flow Equation ??
Hendrik Ranocha and
Jan Nordström A New Class of $A$ Stable Summation by
Parts Time Integration Schemes with
Strong Initial Conditions . . . . . . . ??
Yuwen Li Superconvergent Flux Recovery of the
Rannacher--Turek Nonconforming Element ??
Weihong Guo and
Yifei Lou and
Jing Qin and
Ming Yan A Novel Regularization Based on the
Error Function for Sparse Recovery . . . ??
Hao Chen and
Hai-Wei Sun A Dimensional Splitting Exponential Time
Differencing Scheme for Multidimensional
Fractional Allen--Cahn Equations . . . . ??
Albert Costa-Solé and
Eloi Ruiz-Gironés and
Josep Sarrate High-Order Hybridizable Discontinuous
Galerkin Formulation for One-Phase Flow
Through Porous Media . . . . . . . . . . ??
Xue-Yang Li and
Ai-Guo Xiao Space-Fractional Diffusion Equation with
Variable Coefficients: Well-posedness
and Fourier Pseudospectral Approximation ??
Wenqiang Xiao and
Bo Gong and
Jiguang Sun and
Zhimin Zhang Finite Element Calculation of Photonic
Band Structures for Frequency Dependent
Materials . . . . . . . . . . . . . . . ??
Jilu Wang and
Jungang Wang and
Lihong Yin A Single-Step Correction Scheme of
Crank--Nicolson Convolution Quadrature
for the Subdiffusion Equation . . . . . ??
Hongyu Qin and
Fengyan Wu and
Jiwei Zhang and
Chunlai Mu A Linearized Compact ADI Scheme for
Semilinear Parabolic Problems with
Distributed Delay . . . . . . . . . . . ??
Duo Qiu and
Minru Bai and
Michael K. Ng and
Xiongjun Zhang Robust Low Transformed Multi-Rank Tensor
Methods for Image Alignment . . . . . . ??
Buyang Li and
Shu Ma A High-order Exponential Integrator for
Nonlinear Parabolic Equations with
Nonsmooth Initial Data . . . . . . . . . ??
Thi-Thao-Phuong Hoang and
Hyesuk Lee A Global-in-time Domain Decomposition
Method for the Coupled Nonlinear Stokes
and Darcy Flows . . . . . . . . . . . . ??
Caiying Wu and
Jing Wang and
Jan Harold Alcantara and
Jein-Shan Chen Smoothing Strategy Along with Conjugate
Gradient Algorithm for Signal
Reconstruction . . . . . . . . . . . . . ??
Bing Tan and
Xiaolong Qin and
Jen-Chih Yao Strong Convergence of Self-adaptive
Inertial Algorithms for Solving Split
Variational Inclusion Problems with
Applications . . . . . . . . . . . . . . ??
Bingxin Zhu and
Haijun Wu Preasymptotic Error Analysis of the HDG
Method for Helmholtz Equation with Large
Wave Number . . . . . . . . . . . . . . ??
Shinya Miyajima Computing Enclosures for the Matrix
Mittag-Leffler Function . . . . . . . . ??
Stefania Fresca and
Luca Dede' and
Andrea Manzoni A Comprehensive Deep Learning-Based
Approach to Reduced Order Modeling of
Nonlinear Time-Dependent Parametrized
PDEs . . . . . . . . . . . . . . . . . . ??
Gwanghyun Jo and
Do Y. Kwak and
Young-Ju Lee Locally Conservative Immersed Finite
Element Method for Elliptic Interface
Problems . . . . . . . . . . . . . . . . ??
Qifeng Zhang and
Lingling Liu Convergence and Stability in Maximum
Norms of Linearized Fourth-Order
Conservative Compact Scheme for
Benjamin--Bona--Mahony--Burgers'
Equation . . . . . . . . . . . . . . . . ??
Jogen Dutta and
Bhupen Deka Optimal A Priori Error Estimates for the
Finite Element Approximation of
Dual-Phase-Lag Bio Heat Model in
Heterogeneous Medium . . . . . . . . . . ??
Lexing Ying A Heuristic Independent Particle
Approximation to Determinantal Point
Processes . . . . . . . . . . . . . . . ??
Brian E. Moore Exponential Integrators Based on
Discrete Gradients for Linearly
Damped/Driven Poisson Systems . . . . . ??
Philippe G. LeFloch and
Hendrik Ranocha Kinetic Functions for Nonclassical
Shocks, Entropy Stability, and Discrete
Summation by Parts . . . . . . . . . . . ??
Guanyu Zhou An Analysis on the Finite Volume Schemes
and the Discrete Lyapunov Inequalities
for the Chemotaxis System . . . . . . . ??
Huadong Gao and
Weifeng Qiu The Pointwise Stabilities of Piecewise
Linear Finite Element Method on
Non-obtuse Tetrahedral Meshes of
Nonconvex Polyhedra . . . . . . . . . . ??
Kun Li and
Ting-Zhu Huang and
Liang Li and
Stéphane Lanteri Non-Intrusive Reduced-Order Modeling of
Parameterized Electromagnetic Scattering
Problems using Cubic Spline
Interpolation . . . . . . . . . . . . . ??
Zhonghua Qiao and
Xuguang Yang and
Yuze Zhang A Novel Lattice Boltzmann Model for
Fourth Order Nonlinear Partial
Differential Equations . . . . . . . . . ??
Tie Mei and
Jiangming Zhao and
Zian Liu and
Xuhao Peng and
Ziguang Chen and
Florin Bobaru The Role of Boundary Conditions on
Convergence Properties of Peridynamic
Model for Transient Heat Transfer . . . ??
Konrad Simon and
Jörn Behrens Semi-Lagrangian Subgrid Reconstruction
for Advection-Dominant Multiscale
Problems with Rough Data . . . . . . . . ??
Saray Busto and
Michael Dumbser and
Cipriano Escalante and
Nicolas Favrie and
Sergey Gavrilyuk On High Order ADER Discontinuous
Galerkin Schemes for First Order
Hyperbolic Reformulations of Nonlinear
Dispersive Systems . . . . . . . . . . . ??
Xiaokai Chang and
Junfeng Yang A Golden Ratio Primal--Dual Algorithm
for Structured Convex Optimization . . . ??
Haitao Leng and
Huangxin Chen Adaptive HDG Methods for the Brinkman
Equations with Application to Optimal
Control . . . . . . . . . . . . . . . . ??
Fan Zhang and
Tiegang Liu and
Moubin Liu A High-Order
Maximum-Principle-Satisfying
Discontinuous Galerkin Method for the
Level Set Problem . . . . . . . . . . . ??
Xiaozhi Zhu and
Yong-Tao Zhang Fast Sparse Grid Simulations of Fifth
Order WENO Scheme for High Dimensional
Hyperbolic PDEs . . . . . . . . . . . . ??
Davide Palitta Matrix Equation Techniques for Certain
Evolutionary Partial Differential
Equations . . . . . . . . . . . . . . . ??
Jingwei Li and
Lili Ju and
Yongyong Cai and
Xinlong Feng Unconditionally Maximum Bound Principle
Preserving Linear Schemes for the
Conservative Allen--Cahn Equation with
Nonlocal Constraint . . . . . . . . . . ??
Felipe Lepe and
Enrique Otárola and
Daniel Quero Error Estimates for FEM Discretizations
of the Navier--Stokes Equations with
Dirac Measures . . . . . . . . . . . . . ??
Dongmi Luo and
Jianxian Qiu and
Jun Zhu and
Yibing Chen A Quasi-Conservative Discontinuous
Galerkin Method for Multi-component
Flows Using the Non-oscillatory Kinetic
Flux . . . . . . . . . . . . . . . . . . ??
Kevin Chow and
Steven J. Ruuth Linearly Stabilized Schemes for the Time
Integration of Stiff Nonlinear PDEs . . ??
Minghua Chen and
Fan Yu and
Zhi Zhou Backward Difference Formulae: The Energy
Technique for Subdiffusion Equation . . ??
Le Thi Khanh Hien and
Nicolas Gillis Algorithms for Nonnegative Matrix
Factorization with the Kullback--Leibler
Divergence . . . . . . . . . . . . . . . ??
Hailiang Liu and
Wumaier Maimaitiyiming Efficient, Positive, and Energy Stable
Schemes for Multi-D
Poisson--Nernst--Planck Systems . . . . ??
Erik Burman and
Omar Duran and
Alexandre Ern and
Morgane Steins Convergence Analysis of Hybrid
High-Order Methods for the Wave Equation ??
Thuy T. Le and
Loc H. Nguyen and
Thi-Phong Nguyen and
William Powell The Quasi-reversibility Method to
Numerically Solve an Inverse Source
Problem for Hyperbolic Equations . . . . ??
Yun-Bo Yang and
Yao-Lin Jiang and
Bo-Hao Yu Unconditional Optimal Error Estimates of
Linearized, Decoupled and Conservative
Galerkin FEMs for the
Klein--Gordon--Schrödinger Equation . . . ??
Min Zhang and
Weizhang Huang and
Jianxian Qiu A High-Order Well-Balanced
Positivity-Preserving Moving Mesh DG
Method for the Shallow Water Equations
With Non-Flat Bottom Topography . . . . ??
Wenrui Hao and
Chunyue Zheng A Stochastic Homotopy Tracking Algorithm
for Parametric Systems of Nonlinear
Equations . . . . . . . . . . . . . . . ??
Yilei Shi and
Shusen Xie and
Dong Liang and
Kai Fu High Order Compact Block-Centered Finite
Difference Schemes for Elliptic and
Parabolic Problems . . . . . . . . . . . ??
Jeremy E. Kozdon and
Brittany A. Erickson and
Lucas C. Wilcox Hybridized Summation-by-Parts Finite
Difference Methods . . . . . . . . . . . ??
Xuehai Huang and
Yuling Shi and
Wenqing Wang A Morley--Wang--Xu Element Method for a
Fourth Order Elliptic Singular
Perturbation Problem . . . . . . . . . . ??
Myeongmin Kang and
Miyoun Jung Simultaneous Image Enhancement and
Restoration with Non-convex Total
Variation . . . . . . . . . . . . . . . ??
Maha Youssef and
Roland Pulch Poly-Sinc Solution of Stochastic
Elliptic Differential Equations . . . . ??
Long Teng and
Weidong Zhao High-order Combined Multi-step Scheme
for Solving Forward Backward Stochastic
Differential Equations . . . . . . . . . ??
Mingyan He and
Pengtao Sun Mixed Finite Element Method for Modified
Poisson--Nernst--Planck/Navier--Stokes
Equations . . . . . . . . . . . . . . . ??
Gabriela Jaramillo and
Loic Cappanera and
Cory Ward Numerical Methods for a Diffusive Class
of Nonlocal Operators . . . . . . . . . ??
Daniele Funaro and
Gianmarco Manzini Stability and Conservation Properties of
Hermite-Based Approximations of the
Vlasov--Poisson System . . . . . . . . . ??
Saray Busto and
Michael Dumbser and
Kseniya Ivanova On Thermodynamically Compatible Finite
Volume Methods and Path-Conservative
ADER Discontinuous Galerkin Schemes for
Turbulent Shallow Water Flows . . . . . ??
Jin Zhang and
Xiaowei Liu Convergence and Supercloseness in a
Balanced Norm of Finite Element Methods
on Bakhvalov-Type Meshes for
Reaction--Diffusion Problems . . . . . . ??
Lanyu Lin and
Yong-Jin Liu An Efficient Hessian Based Algorithm for
Singly Linearly and Box Constrained
Least Squares Regression . . . . . . . . ??
Bawfeh Kingsley Kometa and
Naveed Iqbal and
Adel A. Attiya Optimal Parameters for Third Order
Runge--Kutta Exponential Integrators for
Convection--Diffusion Problems . . . . . ??
Hailong Guo and
Xu Yang and
Yi Zhu Unfitted Nitsche's Method for Computing
Wave Modes in Topological Materials . . ??
Luca Bonaventura and
Elisa Calzola and
Roberto Ferretti Second Order Fully Semi-Lagrangian
Discretizations of
Advection--Diffusion--Reaction Systems ??
Moritz Geist and
Philipp Petersen and
Gitta Kutyniok Numerical Solution of the Parametric
Diffusion Equation by Deep Neural
Networks . . . . . . . . . . . . . . . . ??
Antoine Gautier and
Matthias Hein and
Francesco Tudisco The Global Convergence of the Nonlinear
Power Method for Mixed-Subordinate
Matrix Norms . . . . . . . . . . . . . . ??
Xin Li and
Yuezheng Gong and
Luming Zhang Linear High-Order Energy-Preserving
Schemes for the Nonlinear Schrödinger
Equation with Wave Operator Using the
Scalar Auxiliary Variable Approach . . . ??
Nan Wang and
Meng Li and
Chengming Huang Unconditional Energy Dissipation and
Error Estimates of the SAV Fourier
Spectral Method for Nonlinear Fractional
Generalized Wave Equation . . . . . . . ??
Ludvig Lindeberg and
Tuan Dao and
Ken Mattsson A High Order Accurate Finite Difference
Method for the
Drinfel'd--Sokolov--Wilson Equation . . ??
Dong-qin Gu and
Zhong-qing Wang Orthogonal Jacobi Rational Functions and
Spectral Methods on the Half Line . . . ??
Jun Hu and
Hua Wang An Optimal Multigrid Algorithm for the
Combining $ P_1$--$ Q_1$ Finite Element
Approximations of Interface Problems
Based on Local Anisotropic Fitting
Meshes . . . . . . . . . . . . . . . . . ??
Rosanna Campagna and
Emma Perracchione Data-Driven Extrapolation Via Feature
Augmentation Based on Variably Scaled
Thin Plate Splines . . . . . . . . . . . ??
Qiming Wang and
Zhaojie Zhou Adaptive Virtual Element Method for
Optimal Control Problem Governed by
General Elliptic Equation . . . . . . . ??
Christian Parkinson A Rotating-Grid Upwind Fast Sweeping
Scheme for a Class of Hamilton--Jacobi
Equations . . . . . . . . . . . . . . . ??
Yaguang Gu and
Zhen Gao and
Lifeng Wang A Robust High Order Alternative WENO
Scheme for the Five-Equation Model . . . ??
Yong-Liang Zhao and
Xian-Ming Gu and
Alexander Ostermann A Preconditioning Technique for an
All-at-once System from Volterra
Subdiffusion Equations with Graded Time
Steps . . . . . . . . . . . . . . . . . ??
Yangang Chen and
Justin W. L. Wan Artificial Viscosity Joint Spacetime
Multigrid Method for
Hamilton--Jacobi--Bellman and
Kolmogorov--Fokker--Planck System
Arising from Mean Field Games . . . . . ??
Qiwei Sheng and
Cheng Wang A Spherical Harmonic Discontinuous
Galerkin Method for Radiative Transfer
Equations with Vacuum Boundary
Conditions . . . . . . . . . . . . . . . ??
Liang Pan and
Kun Xu An Arbitrary-Lagrangian--Eulerian
High-Order Gas-Kinetic Scheme for
Three-Dimensional Computations . . . . . ??
Alexandre Chiapolino and
François Fraysse and
Richard Saurel A Method to Solve Hamilton--Jacobi Type
Equation on Unstructured Meshes . . . . ??
André Berg and
David Cohen and
Guillaume Dujardin Lie--Trotter Splitting for the Nonlinear
Stochastic Manakov System . . . . . . . ??
Qin Zhou and
Binjie Li Temporally Semidiscrete Approximation of
a Dirichlet Boundary Control for a
Fractional/Normal Evolution Equation
with a Final Observation . . . . . . . . ??
Changtao Sheng and
Duo Cao and
Jie Shen Efficient Spectral Methods for PDEs with
Spectral Fractional Laplacian . . . . . ??
David A. Kopriva and
Gregor J. Gassner and
Jan Nordström Stability of Discontinuous Galerkin
Spectral Element Schemes for Wave
Propagation when the Coefficient
Matrices have Jumps . . . . . . . . . . ??
J. Figueiredo and
S. Clain A MOOD--MUSCL Hybrid Formulation for the
Non-conservative Shallow-Water System ??
Yetong Li and
Tengjin Zhao and
Tongke Wang The High Order Augmented Finite Volume
Methods Based on Series Expansion for
Nonlinear Degenerate Parabolic Equations ??
Yue Feng Improved Error Bounds of the Strang
Splitting Method for the Highly
Oscillatory Fractional Nonlinear
Schrödinger Equation . . . . . . . . . . ??
Peng Li and
Bao-Shan Wang and
Wai-Sun Don Sensitivity Parameter-Independent
Characteristic-Wise Well-Balanced Finite
Volume WENO Scheme for the Euler
Equations Under Gravitational Fields . . ??
Wei Zhu A First-Order Image Restoration Model
that Promotes Image Contrast
Preservation . . . . . . . . . . . . . . ??
Hong Zhu and
Michael K. Ng and
Guang-Jing Song An Approximate Augmented Lagrangian
Method for Nonnegative Low-Rank Matrix
Approximation . . . . . . . . . . . . . ??
Felipe Lepe and
David Mora and
Iván Velásquez A Virtual Element Method for the Steklov
Eigenvalue Problem Allowing Small Edges ??
Xiaowen Shen and
Qi Wang Thermodynamically Consistent Algorithms
for Models of Diblock Copolymer
Solutions Interacting with Electric and
Magnetic Fields . . . . . . . . . . . . ??
Shengxiang Deng and
Hongpeng Sun A Preconditioned Difference of Convex
Algorithm for Truncated Quadratic
Regularization with Application to
Imaging . . . . . . . . . . . . . . . . ??
Haifeng Wang and
Jian-Feng Cai and
Ke Wei Fast Cadzow's Algorithm and a Gradient
Variant . . . . . . . . . . . . . . . . ??
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Corrigenda: Fully Discrete
Approximations to the Time-dependent
Navier--Stokes Equations with a
Projection Method in Time and Grad-div
Stabilization . . . . . . . . . . . . . ??
Xiaodi Zhang and
Qianqian Ding Coupled Iterative Analysis for
Stationary Inductionless
Magnetohydrodynamic System Based on
Charge-Conservative Finite Element
Method . . . . . . . . . . . . . . . . . ??
Dawei Wang and
Yunhui He and
Hans De Sterck On the Asymptotic Linear Convergence
Speed of Anderson Acceleration Applied
to ADMM . . . . . . . . . . . . . . . . ??
Qian-Min Huang and
Yu-Xin Ren and
Qian Wang High Order Finite Volume Schemes for
Solving the Non-Conservative Convection
Equations on the Unstructured Grids . . ??
Alec Dektor and
Abram Rodgers and
Daniele Venturi Rank-Adaptive Tensor Methods for
High-Dimensional Nonlinear PDEs . . . . ??
Erik Burman and
Cuiyu He and
Mats G. Larson Comparison of Shape Derivatives Using
CutFEM for Ill-posed Bernoulli Free
Boundary Problem . . . . . . . . . . . . ??
Andreas Dedner and
Jan Giesselmann and
Jennifer K Ryan Residual Estimates for Post-processors
in Elliptic Problems . . . . . . . . . . ??
Min Wang and
Qiumei Huang and
Cheng Wang A Second Order Accurate Scalar Auxiliary
Variable (SAV) Numerical Method for the
Square Phase Field Crystal Equation . . ??
Maolin Che and
Yimin Wei and
Hong Yan An Efficient Randomized Algorithm for
Computing the Approximate Tucker
Decomposition . . . . . . . . . . . . . ??
Xiaobing Feng and
Hailong Qiu Analysis of Fully Discrete Mixed Finite
Element Methods for Time-dependent
Stochastic Stokes Equations with
Multiplicative Noise . . . . . . . . . . ??
Wayne Isaac Tan Uy and
Benjamin Peherstorfer Operator Inference of Non-Markovian
Terms for Learning Reduced Models from
Partially Observed State Trajectories ??
Shengliang Zhang Meshless Symplectic and Multi-symplectic
Local RBF Collocation Methods for
Hamiltonian PDEs . . . . . . . . . . . . ??
B. Kheirfam A Polynomial-Iteration Infeasible
Interior-Point Algorithm with Arc-Search
for Semidefinite optimization . . . . . ??
Jordi Ventura and
David Codony and
Sonia Fernández-Méndez A C0 Interior Penalty Finite Element
Method for Flexoelectricity . . . . . . ??
Hua Shen and
Matteo Parsani A Rotated Characteristic Decomposition
Technique for High-Order Reconstructions
in Multi-dimensions . . . . . . . . . . ??
Giuseppe Patané Spectrum-Free and Meshless Solvers of
Parabolic PDEs . . . . . . . . . . . . . ??
Prasit Cholamjiak and
Dang Van Hieu and
Yeol Je Cho Relaxed Forward-Backward Splitting
Methods for Solving Variational
Inclusions and Applications . . . . . . ??
Alberto Prieto-Arranz and
Luis Ramírez and
Xesús Nogueira A Well-Balanced SPH-ALE Scheme for
Shallow Water Applications . . . . . . . ??
Qi Xu and
Zaihua Wang and
Li Cheng Calculating Characteristic Roots of
Multi-Delayed Systems with Accumulation
Points via a Definite Integral Method ??
Unjong Yu and
Young-Min Lee and
Chi-Ok Hwang Last-passage Monte Carlo Algorithm for
Charge Density on a Conducting Spherical
Surface . . . . . . . . . . . . . . . . ??
Jiming Yang and
Yifan Su A Two-Grid Combined Mixed Finite Element
and Discontinuous Galerkin Method for an
Incompressible Miscible Displacement
Problem in Porous Media . . . . . . . . ??
Yang Wang and
Yanping Chen and
Huaming Yi A Family of Two-Grid Partially Penalized
Immersed Finite Element Methods for
Semi-linear Parabolic Interface Problems ??
Tommaso Taddei and
Lei Zhang Registration-Based Model Reduction in
Complex Two-Dimensional Geometries . . . ??
Hongliang Li and
Pingbing Ming and
Huiyu Wang $ H^2$--Korn's Inequality and the
Nonconforming Elements for The Strain
Gradient Elastic Model . . . . . . . . . ??
Yuwen Li Recovery-based a Posteriori Error
Analysis for Plate Bending Problems . . ??
El Houssaine Quenjel Analysis of Accurate and Stable
Nonlinear Finite Volume Scheme for
Anisotropic Diffusion Equations with
Drift on Simplicial Meshes . . . . . . . ??
Qin Li and
Pan Yan and
Yancheng You On Developing Piecewise Rational Mapping
with Fine Regulation Capability for WENO
Schemes . . . . . . . . . . . . . . . . ??
Longzhao Qi and
Yanren Hou A Second Order Energy Stable BDF
Numerical Scheme for the
Swift--Hohenberg Equation . . . . . . . ??
Christian Beck and
Sebastian Becker and
Arnulf Jentzen Solving the Kolmogorov PDE by Means of
Deep Learning . . . . . . . . . . . . . ??
Yann-Meing Law and
Jean-Christophe Nave FDTD Schemes for Maxwell's Equations
with Embedded Perfect Electric
Conductors Based on the Correction
Function Method . . . . . . . . . . . . ??
Qianqian Ding and
Xiaonian Long and
Shipeng Mao Error Estimate of a Fully Discrete
Finite Element Method for Incompressible
Vector Potential Magnetohydrodynamic
System . . . . . . . . . . . . . . . . . ??
Buyang Li and
Shu Ma and
Na Wang Second-Order Convergence of the Linearly
Extrapolated Crank--Nicolson Method for
the Navier--Stokes Equations with $
\mathbf {H}^1 $ Initial Data . . . . . . ??
Beichuan Deng and
Jie Shen and
Qingqu Zhuang Second-Order SAV Schemes for the
Nonlinear Schrödinger Equation and Their
Error Analysis . . . . . . . . . . . . . ??
Yuyuan Yan and
Bernard A. Egwu and
Yubin Yan Error Estimates of a Continuous Galerkin
Time Stepping Method for Subdiffusion
Problem . . . . . . . . . . . . . . . . ??
Kejia Pan and
Dongdong He and
Zhilin Li A High Order Compact FD Framework for
Elliptic BVPs Involving Singular
Sources, Interfaces, and Irregular
Domains . . . . . . . . . . . . . . . . ??
Rachid Ait-Haddou Computation of Optimal Linear Strong
Stability Preserving Methods Via
Adaptive Spectral Transformations of
Poisson--Charlier Measures . . . . . . . ??
Yannan Chen and
Xinzhen Zhang and
Yanwei Xu A Barzilai--Borwein Gradient Algorithm
for Spatio-Temporal Internet Traffic
Data Completion via Tensor Triple
Decomposition . . . . . . . . . . . . . 65:1--65:24
Mei-Heng Yueh and
Tsung-Ming Huang and
Shing-Tung Yau Projected Gradient Method Combined with
Homotopy Techniques for
Volume-Measure-Preserving Optimal Mass
Transportation Problems . . . . . . . . ??
Qi Tao and
Waixiang Cao and
Zhimin Zhang Superconvergence Analysis of the
Ultra-Weak Local Discontinuous Galerkin
Method for One Dimensional Linear Fifth
Order Equations . . . . . . . . . . . . ??
Limin Ma Superconvergence of Discontinuous
Galerkin Methods for Elliptic Boundary
Value Problems . . . . . . . . . . . . . ??
Feng Qu and
Di Sun and
Junqiang Bai Low-Speed Modification for the Genuinely
Multidimensional Harten, Lax, van Leer
and Einfeldt Scheme in Curvilinear
Coordinates . . . . . . . . . . . . . . ??
Qi Li and
Liquan Mei Numerical Approximation of the
Two-Component PFC Models for Binary
Colloidal Crystals: Efficient,
Decoupled, and Second-Order
Unconditionally Energy Stable Schemes ??
Taibai Fu and
Beiping Duan and
Zhoushun Zheng An Effective Finite Element Method with
Singularity Reconstruction for
Fractional Convection-diffusion Equation ??
Minghua Chen and
Suzhen Jiang and
Weiping Bu Two $ L_1 $ Schemes on Graded Meshes for
Fractional Feynman--Kac Equation . . . . ??
Weijie Zhang and
Yinhua Xia and
Yan Xu Positivity-Preserving Well-Balanced
Arbitrary Lagrangian--Eulerian
Discontinuous Galerkin Methods for the
Shallow Water Equations . . . . . . . . ??
Xin-long Luo and
Hang Xiao Generalized Continuation Newton Methods
and the Trust-Region Updating Strategy
for the Underdetermined System . . . . . ??
Stefano Giani and
Luka Grubisi\'c and
Jeffrey S. Ovall A Posteriori Error Estimates for
Elliptic Eigenvalue Problems Using
Auxiliary Subspace Techniques . . . . . ??
Kaho Ho and
Shingyu Leung and
Jianliang Qian Fast Huygens Sweeping Methods for a
Class of Nonlocal Schrödinger Equations ??
Zexin Liu and
Akil Narayan On the Computation of Recurrence
Coefficients for Univariate Orthogonal
Polynomials . . . . . . . . . . . . . . ??
Arbaz Khan and
Manil T. Mohan and
Ricardo Ruiz-Baier Conforming, Nonconforming and DG Methods
for the Stationary Generalized
Burgers--Huxley Equation . . . . . . . . ??
Kenneth Duru and
Leonhard Rannabauer and
Heiner Igel A New Discontinuous Galerkin Method for
Elastic Waves with Physically Motivated
Numerical Fluxes . . . . . . . . . . . . ??
Zhongbing Xie and
Gang Cai and
Qiao-Li Dong Strong Convergence of the Modified
Inertial Extragradient Method with
Line-Search Process for Solving
Variational Inequality Problems in
Hilbert Spaces . . . . . . . . . . . . . ??
Yijin Gao and
Jay Mayfield and
Songting Luo A Second-Order Fast Huygens Sweeping
Method for Time-Dependent Schrödinger
Equations with Perfectly Matched Layers ??
Riccardo Tosi and
Ramon Amela and
Riccardo Rossi A Parallel Dynamic Asynchronous
Framework for Uncertainty Quantification
by Hierarchical Monte Carlo Algorithms ??
R. A. M. van Gestel and
M. J. H. Anthonissen and
W. L. IJzerman An Energy Conservative hp-method for
Liouville's Equation of Geometrical
Optics . . . . . . . . . . . . . . . . . ??
Lin Mu and
Xiu Ye and
Shangyou Zhang Development of Pressure-Robust
Discontinuous Galerkin Finite Element
Methods for the Stokes Problem . . . . . ??
Mariana Prazeres and
Adam M. Oberman Stochastic Gradient Descent with
Polyak's Learning Rate . . . . . . . . . ??
Binbin Du and
Jianguo Huang and
Haibiao Zheng Two-Grid Arrow-Hurwicz Methods for the
Steady Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . ??
François Desquilbet and
Jian Cao and
Jean-Marie Mirebeau Single Pass Computation of First Seismic
Wave Travel Time in Three Dimensional
Heterogeneous Media With General
Anisotropy . . . . . . . . . . . . . . . ??
Nicola Guglielmi and
María López-Fernández and
Mattia Manucci Pseudospectral Roaming Contour Integral
Methods for Convection--Diffusion
Equations . . . . . . . . . . . . . . . ??
Sung Woong Cho and
Hyung Ju Hwang and
Hwijae Son Traveling Wave Solutions of Partial
Differential Equations Via Neural
Networks . . . . . . . . . . . . . . . . ??
Pietro Benedusi and
Paola Ferrari and
Stefano Serra-Capizzano Fast Parallel Solver for the Space-time
IgA-DG Discretization of the Diffusion
Equation . . . . . . . . . . . . . . . . ??
Marcella Bonazzoli and
Xavier Claeys and
Pierre-Henri Tournier Analysis of the SORAS Domain
Decomposition Preconditioner for
Non-self-adjoint or Indefinite Problems ??
Yang Liu and
Baoli Yin and
Zhimin Zhang The Unified Theory of Shifted
Convolution Quadrature for Fractional
Calculus . . . . . . . . . . . . . . . . ??
Jea-Hyun Park and
Abner J. Salgado and
Steven M. Wise Preconditioned Accelerated Gradient
Descent Methods for Locally Lipschitz
Smooth Objectives with Applications to
the Solution of Nonlinear PDEs . . . . . ??
Mehdi Dehghan and
Zeinab Gharibi Virtual Element Method for Solving an
Inhomogeneous Brusselator Model With and
Without Cross-Diffusion in Pattern
Formation . . . . . . . . . . . . . . . ??
Hongjia Chen and
Kuan Xu On the Backward Error Incurred by the
Compact Rational Krylov Linearization ??
Eduard Feireisl and
Madalina Petcu and
Bangwei She Numerical Analysis of a Model of Two
Phase Compressible Fluid Flow . . . . . ??
Huan-Yan Jian and
Ting-Zhu Huang and
Yong-Liang Zhao Fast IIF-WENO Method on Non-uniform
Meshes for Nonlinear Space-Fractional
Convection--Diffusion--Reaction
Equations . . . . . . . . . . . . . . . ??
Shuting Gu and
Ling Lin and
Xiang Zhou Projection Method for Saddle Points of
Energy Functional in $ H^{-1} $ Metric ??
Siavash Hedayati Nasab and
Carlos A. Pereira and
Brian C. Vermeire Optimal Runge--Kutta Stability
Polynomials for Multidimensional
High-Order Methods . . . . . . . . . . . ??
Xin-Hui Shao and
Yu-Han Li and
Hai-Long Shen Quasi-Toeplitz Trigonometric Transform
Splitting Methods for Spatial Fractional
Diffusion Equations . . . . . . . . . . ??
Efthymios N. Karatzas and
Gianluigi Rozza A Reduced Order Model for a Stable
Embedded Boundary Parametrized
Cahn--Hilliard Phase-Field System Based
on Cut Finite Elements . . . . . . . . . ??
Weimin Han and
Kenneth Czuprynski and
Feifei Jing Mixed Finite Element Method for a
Hemivariational Inequality of Stationary
Navier--Stokes Equations . . . . . . . . ??
Xinyuan Liu and
Yang Yang and
Hui Guo High-Order Bound-Preserving Finite
Difference Methods for Incompressible
Wormhole Propagation . . . . . . . . . . ??
Ho Law and
Chun Yin Siu and
Lok Ming LUI Decomposition of Longitudinal
Deformations via Beltrami Descriptors ??
Yaguang Gu and
Felix Kwok On the Choice of Robin Parameters for
the Optimized Schwarz Method for Domains
with Non-Conforming Heterogeneities . . ??
Zhen-Ping Yang and
Jin Zhang and
Gui-Hua Lin Variance-Based Subgradient Extragradient
Method for Stochastic Variational
Inequality Problems . . . . . . . . . . ??
Philippe G. LeFloch and
Carlos Parés and
Ernesto Pimentel-García A Class of Well-Balanced Algorithms for
Relativistic Fluids on a Schwarzschild
Background . . . . . . . . . . . . . . . ??
David A. Kopriva and
Gregor J. Gassner A Split-form, Stable CG/DG-SEM for Wave
Propagation Modeled by Linear Hyperbolic
Systems . . . . . . . . . . . . . . . . ??
Liliana Borcea and
Vladimir Druskin and
Jörn Zimmerling A Reduced Order Model Approach to
Inverse Scattering in Lossy Layered
Media . . . . . . . . . . . . . . . . . ??
Jesse Chan and
Mario J. Bencomo and
David C. Del Rey Fernández Mortar-based Entropy-Stable
Discontinuous Galerkin Methods on
Non-conforming Quadrilateral and
Hexahedral Meshes . . . . . . . . . . . ??
Aysegül Keten Çopur and
Emirhan Hacioglu and
Müzeyyen Ertürk An Efficient Inertial Type Iterative
Algorithm to Approximate the Solutions
of Quasi Variational Inequalities in
Real Hilbert Spaces . . . . . . . . . . ??
Pin Lyu and
Seakweng Vong Second-Order and Nonuniform
Time-Stepping Schemes for Time
Fractional Evolution Equations with
Time-Space Dependent Coefficients . . . ??
Alina Chertock and
Shaoshuai Chu and
Alexander Kurganov Hybrid Multifluid Algorithms Based on
the Path-Conservative Central-Upwind
Scheme . . . . . . . . . . . . . . . . . ??
Yanrong Zhang and
Jie Shen Efficient Structure Preserving Schemes
for the Klein--Gordon-Schrödinger
Equations . . . . . . . . . . . . . . . ??
Stefania Bellavia and
Jacek Gondzio and
Margherita Porcelli A Relaxed Interior Point Method for
Low-Rank Semidefinite Programming
Problems with Applications to Matrix
Completion . . . . . . . . . . . . . . . ??
Maohui Lyu and
Vrushali A. Bokil and
Fengyan Li Energy Stable Nodal Discontinuous
Galerkin Methods for Nonlinear Maxwell's
Equations in Multi-dimensions . . . . . ??
Gianluca Fabiani and
Francesco Calabr\`o and
Constantinos Siettos Numerical solution and bifurcation
analysis of nonlinear partial
differential equations with extreme
learning machines . . . . . . . . . . . ??
Shan Jiang and
Haijun Yu Efficient Spectral Methods for
Quasi-Equilibrium Closure Approximations
of Symmetric Problems on Unit Circle and
Sphere . . . . . . . . . . . . . . . . . ??
Shaoqiang Tang and
Gang Pang Accurate Boundary Treatment for Riesz
Space Fractional Diffusion Equations . . ??
Maxim Olshanskii and
Annalisa Quaini and
Qi Sun An Unfitted Finite Element Method for
Two-Phase Stokes Problems with Slip
Between Phases . . . . . . . . . . . . . ??
Xiaofei Zhao Numerical Integrators for Continuous
Disordered Nonlinear Schrödinger Equation ??
Ram Manohar and
Rajen Kumar Sinha A Posteriori Error Estimates for
Parabolic Optimal Control Problems with
Controls Acting on Lower Dimensional
Manifolds . . . . . . . . . . . . . . . ??
Sebastian Franz Singularly Perturbed Reaction--Diffusion
Problems as First order systems . . . . ??
Seungil Kim and
Hui Zhang Convergence Analysis of the Continuous
and Discrete Non-overlapping Double
Sweep Domain Decomposition Method Based
on PMLs for the Helmholtz Equation . . . ??
Shaohong Du and
Zhiqiang Cai Adaptive Finite Element Method for
Dirichlet Boundary Control of Elliptic
Partial Differential Equations . . . . . ??
Weiming Li and
Peng Song and
Yanli Wang A Hybrid Moment Method for Multi-scale
Kinetic Equations Based on Maximum
Entropy Principle . . . . . . . . . . . ??
Makoto Mizuguchi and
Mitsuhiro T. Nakao and
Shin'ichi Oishi Error Constants for the Semi-Discrete
Galerkin Approximation of the Linear
Heat Equation . . . . . . . . . . . . . ??
Dong Li and
Chaoyu Quan and
Wen Yang The BDF3/EP3 Scheme for MBE with No
Slope Selection is Stable . . . . . . . ??
Zhensheng Sun and
Yu Hu and
Kai Mao An Optimal Finite Difference Scheme with
Minimized Dispersion and Adaptive
Dissipation Considering the Spectral
Properties of the Fully Discrete Scheme ??
Sixtine Michel and
Davide Torlo and
Rémi Abgrall Spectral Analysis of Continuous FEM for
Hyperbolic PDEs: Influence of
Approximation, Stabilization, and
Time-Stepping . . . . . . . . . . . . . ??
Sofia Eriksson Inverses of SBP-SAT Finite Difference
Operators Approximating the First and
Second Derivative . . . . . . . . . . . ??
Benjamin Yeager and
Ethan Kubatko and
Dylan Wood Time Step Restrictions for
Strong-Stability-Preserving Multistep
Runge--Kutta Discontinuous Galerkin
Methods . . . . . . . . . . . . . . . . ??
Minghui Li and
Wen Li and
Mingqing Xiao The Nonconvex Tensor Robust Principal
Component Analysis Approximation Model
via the Weighted $ \ell_p$-Norm
Regularization . . . . . . . . . . . . . ??
D. Fishelov and
J.-P. Croisille Optimal Convergence for Time-Dependent
Stokes Equation: a New Approach . . . . ??
Hongyu Qin and
Dongfang Li and
Zhimin Zhang A Novel Scheme to Capture the Initial
Dramatic Evolutions of Nonlinear
Subdiffusion Equations . . . . . . . . . ??
Panagiotis Tsoutsanis and
Ebenezer Mayowa Adebayo and
Martin Skote CWENO Finite-Volume Interface Capturing
Schemes for Multicomponent Flows Using
Unstructured Meshes . . . . . . . . . . ??
Sridhar Chellappa and
Lihong Feng and
Peter Benner A Training Set Subsampling Strategy for
the Reduced Basis Method . . . . . . . . ??
Dong Li and
Chaoyu Quan and
Wen Yang Correction to: The BDF3/EP3 Scheme for
MBE with No Slope Selection is Stable ??
Lihong Feng and
Guosheng Fu and
Zhu Wang A FOM/ROM Hybrid Approach for
Accelerating Numerical Simulations . . . ??
YuFeng Shi and
Yan Guo An Essential Seventh-Order Weighted
Compact Adaptive Scheme for Hyperbolic
Conservation Laws . . . . . . . . . . . ??
Jia Yin and
Chunxiong Zheng Space Reduction for Linear Systems with
Local Symmetry . . . . . . . . . . . . . ??
Jongho Park Accelerated Additive Schwarz Methods for
Convex Optimization with Adaptive
Restart . . . . . . . . . . . . . . . . ??
Jing Zhang and
Shengfeng Zhu and
Xiaoqin Shen A Two-Grid Binary Level Set Method for
Eigenvalue Optimization . . . . . . . . ??
Kevin Kamm and
Stefano Pagliarani and
Andrea Pascucci On the Stochastic Magnus Expansion and
Its Application to SPDEs . . . . . . . . ??
Cipriano Escalante Sánchez and
Enrique D. Fernández-Nieto and
Jacques Sainte-Marie Numerical Simulations of a Dispersive
Model Approximating Free-Surface Euler
Equations . . . . . . . . . . . . . . . ??
Xue-lei Lin and
Michael K. Ng Image Completion and Blind
Deconvolution: Model and Algorithm . . . ??
Hui Xie and
Xuejun Xu and
Heng Yong A Positivity-Preserving Finite Volume
Scheme with Least Square Interpolation
for 3D Anisotropic Diffusion Equation ??
Yaguang Gu and
Zhen Gao and
Lifeng Wang High Order Finite Difference Alternative
WENO Scheme for Multi-component Flows ??
Tong Zhang and
JinYun Yuan Unconditional Stability and Optimal
Error Estimates of Euler
Implicit/Explicit-SAV Scheme for the
Navier--Stokes Equations . . . . . . . . ??
Ryan G. McClarren and
James A. Rossmanith and
Minwoo Shin Semi-implicit Hybrid Discrete $ H^T_N $
Approximation of Thermal Radiative
Transfer . . . . . . . . . . . . . . . . ??
Xiaoxue Qin and
Luchan Zhang and
Yang Xiang A Three-Dimensional Continuum Simulation
Method for Grain Boundary Motion
Incorporating Dislocation Structure . . ??
Hengbin An and
Zeyao Mo and
Xiaowen Xu Shear Decoupled Parallel Scalable
Preconditioners for Nonlinear
Thermo-Mechanical Coupled Contact
Applications . . . . . . . . . . . . . . ??
Federico Vismara and
Tommaso Benacchio and
Luca Bonaventura A Seamless, Extended DG Approach for
Advection--Diffusion Problems on
Unbounded Domains . . . . . . . . . . . ??
Lin Lu and
Qi Wang and
Yushun Wang Local Energy Dissipation Rate Preserving
Approximations to Driven Gradient Flows
with Applications to Graphene Growth . . ??
Yakui Huang and
Yu-Hong Dai and
Hongchao Zhang On the Asymptotic Convergence and
Acceleration of Gradient Methods . . . . ??
Hong Zhang and
Jingye Yan and
Songhe Song Explicit Third-Order Unconditionally
Structure-Preserving Schemes for
Conservative Allen--Cahn Equations . . . ??
Alina Chertock and
Alexander Kurganov and
Tong Wu Well-Balancing via Flux Globalization:
Applications to Shallow Water Equations
with Wet/Dry Fronts . . . . . . . . . . ??
G. N. Ogwo and
C. Izuchukwu and
O. T. Mewomo Convergence of Relaxed Inertial
Subgradient Extragradient Methods for
Quasimonotone Variational Inequality
Problems . . . . . . . . . . . . . . . . ??
Yifei Wang and
Wuchen Li Accelerated Information Gradient Flow ??
Alessandro Alla and
Carmen Gräßle and
Michael Hinze Time Adaptivity in Model Predictive
Control . . . . . . . . . . . . . . . . ??
Christina Frederick and
Magnus Egerstedt and
Haomin Zhou Collective Motion Planning for a Group
of Robots Using Intermittent Diffusion ??
Gary P. T. Choi and
Yechen Liu and
Lok Ming Lui Free-Boundary Conformal Parameterization
of Point Clouds . . . . . . . . . . . . ??
Huan Liu and
Xiangcheng Zheng and
Hongfei Fu Error Estimate of Finite Element
Approximation for Two-Sided
Space-Fractional Evolution Equation with
Variable Coefficient . . . . . . . . . . ??
Luling Cao and
Yinnian He and
Jian Li A Parallel Robin--Robin Domain
Decomposition Method based on Modified
Characteristic FEMs for the
Time-Dependent
Dual-porosity-Navier--Stokes Model with
the Beavers--Joseph Interface Condition ??
Yinnian He and
Xiaojing Dong and
Xinlong Feng Uniform Stability and Convergence with
Respect to $ (\nu, \mu, s, 1 - \sigma) $
of the Three Iterative Finite Element
Solutions for the 3D Steady MHD
Equations . . . . . . . . . . . . . . . ??
Bo Dong The Homotopy Method for the Complete
Solution of Quadratic Two-parameter
Eigenvalue Problems . . . . . . . . . . ??
Xing Liu High-Accuracy Time Discretization of
Stochastic Fractional Diffusion Equation ??
Yafei Sun and
Shu-Lin Wu and
Yingxiang Xu A Parallel-in-Time Implementation of the
Numerov Method For Wave Equations . . . ??
Lingling Zhou and
Yinhua Xia Arbitrary Lagrangian--Eulerian Local
Discontinuous Galerkin Method for Linear
Convection--Diffusion Equations . . . . ??
R. Diaz-Adame and
S. Jerez and
H. Carrillo Fast and Optimal WENO Schemes for
Degenerate Parabolic Conservation Laws ??
Paola F. Antonietti and
Lorenzo Mascotto and
Stefano Zonca Stability Analysis of Polytopic
Discontinuous Galerkin Approximations of
the Stokes Problem with Applications to
Fluid-Structure Interaction Problems . . ??
Yanyan Wang and
Zhaopeng Hao and
Rui Du A Linear Finite Difference Scheme for
the Two-Dimensional Nonlinear Schrödinger
Equation with Fractional Laplacian . . . ??
Dianming Hou and
Chuanju Xu A Second Order Energy Dissipative Scheme
for Time Fractional $ L^2 $ Gradient
Flows using SAV Approach . . . . . . . . ??
Fang Li and
Yamin Ru and
Xiao-Guang Lv Patch-Based Weighted SCAD Prior for
Rician Noise Removal . . . . . . . . . . ??
Wanwan Zhu and
Ying Yang and
Benzhuo Lu Residual Type A Posteriori Error
Estimates for the Time-Dependent
Poisson--Nernst--Planck Equations . . . ??
Paola Bacigaluppi and
Julien Carlier and
Rémi Abgrall Assessment of a Non-Conservative
Four-Equation Multiphase System with
Phase Transition . . . . . . . . . . . . ??
Shuhao Cao and
Long Chen and
Xuehai Huang Error Analysis of a Decoupled Finite
Element Method for Quad-Curl Problems ??
Enrico Meli and
Benedetta Morini and
Cristina Sgattoni Solving Nonlinear Systems of Equations
Via Spectral Residual Methods: Stepsize
Selection and Applications . . . . . . . ??
Weina Wang and
Yunmei Chen An Accelerated Smoothing Gradient Method
for Nonconvex Nonsmooth Minimization in
Image Processing . . . . . . . . . . . . ??
Vladimir Druskin and
Alexander V. Mamonov and
Mikhail Zaslavsky Distance Preserving Model Order
Reduction of Graph-Laplacians and
Cluster Analysis . . . . . . . . . . . . ??
T. Aryeni and
Q. Deng and
V. Ginting On the Application of Stable Generalized
Finite Element Method for Quasilinear
Elliptic Two-Point BVP . . . . . . . . . ??
Xue Jiang and
Xiaoqi Duan A PML Finite Element Method for
Electromagnetic Scattering Problems in a
Two-Layer Medium . . . . . . . . . . . . ??
Brittany Froese Hamfeldt and
Jacob Lesniewski Convergent Finite Difference Methods for
Fully Nonlinear Elliptic Equations in
Three Dimensions . . . . . . . . . . . . ??
Mohammed Yusuf Waziri and
Kabiru Ahmed Two Descent Dai--Yuan Conjugate Gradient
Methods for Systems of Monotone
Nonlinear Equations . . . . . . . . . . ??
Hong Zhu and
Michael K. Ng and
Guang-Jing Song Correction to: An Approximate Augmented
Lagrangian Method for Nonnegative
Low-Rank Matrix Approximation . . . . . ??
Jianfeng Lu and
Cody Murphey and
Stefan Steinerberger Fast Localization of Eigenfunctions via
Smoothed Potentials . . . . . . . . . . ??
Pengfei Jin and
Tianhao Lai and
Bin Dong NPTC-net: Narrow-Band Parallel Transport
Convolutional Neural Networks on Point
Clouds . . . . . . . . . . . . . . . . . ??
Eduardo Abreu and
Jean François and
John Pérez A Class of Positive Semi-discrete
Lagrangian--Eulerian Schemes for
Multidimensional Systems of Hyperbolic
Conservation Laws . . . . . . . . . . . ??
A. S. Hendy and
K. Van Bockstal On a Reconstruction of a Solely
Time-Dependent Source in a
Time-Fractional Diffusion Equation with
Non-smooth Solutions . . . . . . . . . . ??
Zelalem Arega Worku and
David W. Zingg Stability and Functional
Superconvergence of Narrow-Stencil
Second-Derivative Generalized
Summation-By-Parts Discretizations . . . ??
Guangzhi Du and
Liyun Zuo and
Yuhong Zhang A New Local and Parallel Finite Element
Method for the Coupled Stokes--Darcy
Model . . . . . . . . . . . . . . . . . ??
Chaobao Huang and
Hu Chen and
Na An $ \beta $ -Robust Superconvergent
Analysis of a Finite Element Method for
the Distributed Order Time-Fractional
Diffusion Equation . . . . . . . . . . . ??
Nicola Ferro and
Simona Perotto and
Andrea Cangiani An Anisotropic Recovery-Based Error
Estimator for Adaptive Discontinuous
Galerkin Methods . . . . . . . . . . . . ??
Dongmi Luo and
Shiyi Li and
Yibing Chen A Quasi-Conservative Discontinuous
Galerkin Method for Multi-component
Flows Using the Non-oscillatory Kinetic
Flux II: ALE Framework . . . . . . . . . ??
Yuan Li and
Rong An Unconditionally Optimal Error Analysis
of a Linear Euler FEM Scheme for the
Navier--Stokes Equations with Mass
Diffusion . . . . . . . . . . . . . . . ??
S. R. Siva Prasad Kochi and
M. Ramakrishna A Compact Subcell WENO Limiting Strategy
Using Immediate Neighbors for
Runge--Kutta Discontinuous Galerkin
Methods for Unstructured Meshes . . . . ??
Pengfei Huang and
Qingzhi Yang Newton-Based Methods for Finding the
Positive Ground State of
Gross--Pitaevskii Equations . . . . . . ??
Franco Dassi and
Alessio Fumagalli and
Giuseppe Vacca A Virtual Element Method for the Wave
Equation on Curved Edges in Two
Dimensions . . . . . . . . . . . . . . . ??
Hyun Geun Lee and
Jaemin Shin and
June-Yub Lee A High-Order and Unconditionally Energy
Stable Scheme for the Conservative
Allen--Cahn Equation with a Nonlocal
Lagrange Multiplier . . . . . . . . . . ??
E. Guerrero Fernández and
M. J. Castro Díaz and
T. Morales de Luna An Arbitrary High Order Well-Balanced
ADER-DG Numerical Scheme for the
Multilayer Shallow-Water Model with
Variable Density . . . . . . . . . . . . ??
Andreas A. Buchheit and
Torsten Keßler On the Efficient Computation of Large
Scale Singular Sums with Applications to
Long-Range Forces in Crystal Lattices ??
Jochen Schütz and
David C. Seal and
Jonas Zeifang Parallel-in-Time High-Order
Multiderivative IMEX Solvers . . . . . . ??
Lin Fu An Efficient Low-Dissipation High-Order
TENO Scheme for MHD Flows . . . . . . . ??
Jianwei Zhou and
Huiyuan Li and
Zhimin Zhang A Posteriori Error Estimates of Spectral
Approximations for Second Order Partial
Differential Equations in Spherical
Geometries . . . . . . . . . . . . . . . ??
Linwei Fan and
Huiyu Li and
Caiming Zhang Two-Stage Image Denoising via an
Enhanced Low-Rank Prior . . . . . . . . ??
Francesco Colibazzi and
Damiana Lazzaro and
Andrea Samoré Learning Nonlinear Electrical Impedance
Tomography . . . . . . . . . . . . . . . ??
Lothar Reichel and
Ugochukwu O. Ugwu Tensor Arnoldi-Tikhonov and GMRES-Type
Methods for Ill-Posed Problems with a
t-Product Structure . . . . . . . . . . ??
Alessandro Buccini Fast Alternating Direction Multipliers
Method by Generalized Krylov Subspaces ??
Waixiang Cao and
Qingsong Zou Analysis of Spectral Volume Methods for
1D Linear Scalar Hyperbolic Equations ??
Dong Li and
Chaoyu Quan The Operator-Splitting Method for
Cahn--Hilliard is Stable . . . . . . . . ??
Haiyan Su and
Guo-Dong Zhang Highly Efficient and Energy Stable
Schemes for the 2D/3D Diffuse Interface
Model of Two-Phase Magnetohydrodynamics ??
Raynold Tan and
Andrew Ooi Two Dimensional Analysis and
Optimization of Hybrid MDCD-TENO Schemes ??
Min Tang and
Lina Chang and
Yihong Wang Tailored Finite Point Method for
Diffusion Equations with Interfaces on
Distorted Meshes . . . . . . . . . . . . ??
Chaolong Jiang and
Jin Cui and
Songhe Song High-Order Linearly Implicit
Structure-Preserving Exponential
Integrators for the Nonlinear Schrödinger
Equation . . . . . . . . . . . . . . . . ??
Félix del Teso and
Erik Lindgren A Finite Difference Method for the
Variational $p$-Laplacian . . . . . . . ??
Zhipeng Yang and
Ju Ming and
Xiaoming He A Multigrid Multilevel Monte Carlo
Method for Stokes--Darcy Model with
Random Hydraulic Conductivity and
Beavers--Joseph Condition . . . . . . . ??
Yu Zhang and
Songsong Li and
Shan Du Image Multiplicative Denoising Using
Adaptive Euler's Elastica as the
Regularization . . . . . . . . . . . . . ??
Xiaodi Zhang and
Xiaorong Wang A Fully Divergence-Free Finite Element
Scheme for Stationary Inductionless
Magnetohydrodynamic Equations . . . . . ??
Yonghong Yao and
Olaniyi S. Iyiola and
Yekini Shehu Subgradient Extragradient Method with
Double Inertial Steps for Variational
Inequalities . . . . . . . . . . . . . . ??
Xiaobing Feng and
Yan Luo and
Zhu Wang An Efficient Iterative Method for
Solving Parameter-Dependent and Random
Convection--Diffusion Problems . . . . . ??
D. Avijit and
S. Natesan An Efficient DWR-Type a Posteriori Error
Bound of SDFEM for Singularly Perturbed
Convection--Diffusion PDEs . . . . . . . ??
Hassan Bozorgmanesh and
Masoud Hajarian Triangular Decomposition of CP Factors
of a Third-Order Tensor with Application
to Solving Nonlinear Systems of
Equations . . . . . . . . . . . . . . . ??
Lukas Herrmann and
Joost A. A. Opschoor and
Christoph Schwab Constructive Deep ReLU Neural Network
Approximation . . . . . . . . . . . . . ??
Jiang Yang and
Zhaoming Yuan and
Zhi Zhou Arbitrarily High-Order Maximum Bound
Preserving Schemes with Cut-off
Postprocessing for Allen--Cahn Equations ??
Cuixia Niu and
Heping Ma and
Dong Liang Energy-Conserved Splitting Multidomain
Legendre--Tau Spectral Method for Two
Dimensional Maxwell's Equations . . . . ??
Edward Laughton and
Vidhi Zala and
David Moxey Fast Barycentric-Based Evaluation Over
Spectral/$ h p $ Elements . . . . . . . ??
Gregor J. Gassner and
Magnus Svärd and
Florian J. Hindenlang Stability Issues of Entropy-Stable
and/or Split-form High-order Schemes . . ??
R. A. M. van Gestel and
M. J. H. Anthonissen and
W. L. IJzerman Correction to: An Energy Conservative
\em hp-method for Liouville's Equation
of Geometrical Optics . . . . . . . . . ??
Yingxia Xi and
Xia Ji A New Method using $ C^0 $ IPG for the
Biharmonic Eigenvalue Problem . . . . . ??
Allen Alvarez Loya and
Daniel Appelö A Hermite Method with a Discontinuity
Sensor for Hamilton--Jacobi Equations ??
Lina Zhao and
Dohyun Kim and
Eric Chung Staggered DG Method with Small Edges for
Darcy Flows in Fractured Porous Media ??
Pei Fu and
Thomas Frachon and
Sara Zahedi High Order Discontinuous Cut Finite
Element Methods for Linear Hyperbolic
Conservation Laws with an Interface . . ??
P. B. Ryzhakov and
J. Marti and
N. Dialami A Unified Arbitrary Lagrangian--Eulerian
Model for Fluid-Structure Interaction
Problems Involving Flows in Flexible
Channels . . . . . . . . . . . . . . . . ??
Julius Reiss Pressure-Tight and Non-stiff Volume
Penalization for Compressible Flows . . ??
Xin Xu and
Xiaopeng Luo Adaptive Sparse Approximations of
Scattered Data . . . . . . . . . . . . . ??
Shuangshuang Chen and
Qiumei Huang and
Fei Xu A Two-Grid Decoupled Algorithm for a
Multi-Dimensional Darcy--Brinkman
Fracture Model . . . . . . . . . . . . . ??
Fang Feng and
Weimin Han and
Jianguo Huang A Nonconforming Virtual Element Method
for a Fourth-order Hemivariational
Inequality in Kirchhoff Plate Problem ??
Xiaoli Li and
Hongxing Rui Superconvergence of MAC Scheme for a
Coupled Free Flow-Porous Media System
with Heat Transport on Non-uniform Grids ??
Hao Han and
Chengjian Zhang One-parameter Galerkin Finite Element
Methods for Neutral Reaction-diffusion
Equations with Piecewise Continuous
Arguments . . . . . . . . . . . . . . . ??
Nestor Sánchez and
Tonatiuh Sánchez-Vizuet and
Manuel Solano Error Analysis of an Unfitted HDG Method
for a Class of Non-linear Elliptic
Problems . . . . . . . . . . . . . . . . ??
Bin Wang and
Yaolin Jiang Optimal Convergence and Long-Time
conservation of Exponential Integration
for Schrödinger Equations in a Normal or
Highly Oscillatory Regime . . . . . . . ??
Jürgen Dölz and
Olena Palii and
Matthias Schlottbom On Robustly Convergent and Efficient
Iterative Methods for Anisotropic
Radiative Transfer . . . . . . . . . . . ??
Liangshao Hou and
Xun Qian and
Jie Sun An Interior Point Parameterized Central
Path Following Algorithm for Linearly
Constrained Convex Programming . . . . . ??
Jeremy Chouchoulis and
Jochen Schütz and
Jonas Zeifang Jacobian-Free Explicit Multiderivative
Runge--Kutta Methods for Hyperbolic
Conservation Laws . . . . . . . . . . . ??
Walter Boscheri and
Maurizio Tavelli and
Lorenzo Pareschi On the Construction of Conservative
Semi-Lagrangian IMEX Advection Schemes
for Multiscale Time Dependent PDEs . . . ??
Wanrong Cao and
Zhaopeng Hao and
Zhongqiang Zhang Optimal Strong Convergence of Finite
Element Methods for One-Dimensional
Stochastic Elliptic Equations with
Fractional Noise . . . . . . . . . . . . ??
Buyang Li and
Weifeng Qiu and
Zongze Yang A Convergent Post-processed
Discontinuous Galerkin Method for
Incompressible Flow with Variable
Density . . . . . . . . . . . . . . . . ??
Cheng Wang and
Wanli Wang and
Fuyu Zhao A Local Curvature Based Adaptive
Particle Level Set Method . . . . . . . ??
Pascal Mossier and
Andrea Beck and
Claus-Dieter Munz A $p$-Adaptive Discontinuous Galerkin
Method with $ h p$-Shock Capturing . . . ??
Zhichao Peng and
Yanlai Chen and
Fengyan Li A Reduced Basis Method for Radiative
Transfer Equation . . . . . . . . . . . ??
R. Bevilacqua and
G. M. Del Corso and
L. Gemignani Orthogonal Iterations on Companion-Like
Pencils . . . . . . . . . . . . . . . . ??
Ad\`ele Veilleux and
Guillaume Puigt and
Guillaume Daviller Stable Spectral Difference Approach
Using Raviart--Thomas Elements for 3D
Computations on Tetrahedral Grids . . . ??
A. Bermúdez and
B. López-Rodríguez and
P. Venegas Numerical Solution of an Axisymmetric
Eddy Current Model with Current and
Voltage Excitations . . . . . . . . . . ??
Alexander Ostermann and
Fangyan Yao A Fully Discrete Low-Regularity
Integrator for the Nonlinear Schrödinger
Equation . . . . . . . . . . . . . . . . ??
Sergii Kivva Entropy Stable Flux Correction for
Scalar Hyperbolic Conservation Laws . . ??
Yuan Xu and
Di Zhao and
Qiang Zhang Local Error Estimates for Runge--Kutta
Discontinuous Galerkin Methods with
Upwind-Biased Numerical Fluxes for a
Linear Hyperbolic Equation in
One-Dimension with Discontinuous Initial
Data . . . . . . . . . . . . . . . . . . ??
Xuhao Diao and
Jun Hu and
Suna Ma Preconditioned Legendre Spectral
Galerkin Methods for the Non-separable
Elliptic Equation . . . . . . . . . . . ??
Hong Zhang and
Jingye Yan and
Songhe Song Correction to: Explicit Third-Order
Unconditionally Structure-Preserving
Schemes for Conservative Allen--Cahn
Equations . . . . . . . . . . . . . . . ??
Hao Luo and
Xiaoping Xie Optimal Error Estimates of a
Time-Spectral Method for Fractional
Diffusion Problems with Low Regularity
Data . . . . . . . . . . . . . . . . . . ??
Xiao Liu and
Jianlin Xia and
Xiaofeng Ou Interconnected Hierarchical Structures
for Fast Direct Elliptic Solution . . . ??
Ion Victor Gosea and
Serkan Gugercin Data-Driven Modeling of Linear Dynamical
Systems with Quadratic Output in the AAA
Framework . . . . . . . . . . . . . . . ??
Ram Manohar and
Rajen Kumar Sinha Local a Posteriori Error Analysis of
Finite Element Method for Parabolic
Boundary Control Problems . . . . . . . ??
Jiahua Jiang and
Fatoumata Sanogo and
Carmeliza Navasca Low-CP-Rank Tensor Completion via
Practical Regularization . . . . . . . . ??
Yang Liu and
Mark Sussman and
Kourosh Shoele A Novel Supermesh Method for Computing
Solutions to the Multi-material Stefan
Problem with Complex Deforming
Interfaces and Microstructure . . . . . ??
Yanjun Li and
Hai Bi and
Yidu Yang The a Priori and a Posteriori Error
Estimates of DG Method for the Steklov
Eigenvalue Problem in Inverse Scattering ??
Dmitri Kuzmin and
Manuel Quezada de Luna and
Johanna Grüll Bound-preserving Flux Limiting for
High-Order Explicit Runge--Kutta Time
Discretizations of Hyperbolic
Conservation Laws . . . . . . . . . . . ??
Lueling Jia and
Huiyuan Li and
Zhimin Zhang Sparse Spectral-Galerkin Method on An
Arbitrary Tetrahedron Using Generalized
Koornwinder Polynomials . . . . . . . . ??
D. Adak and
D. Mora and
S. Natarajan Convergence Analysis of Virtual Element
Method for Nonlinear Nonlocal Dynamic
Plate Equation . . . . . . . . . . . . . ??
Matthew M. Lin and
Moody T. Chu Rank-1 Approximation for Entangled
Multipartite Real Systems . . . . . . . ??
X. Antoine and
E. Lorin Generalized Fractional Algebraic Linear
System Solvers . . . . . . . . . . . . . ??
Yann-Meing Law and
Jean-Christophe Nave High-Order FDTD Schemes for Maxwell's
Interface Problems with Discontinuous
Coefficients and Complex Interfaces
Based on the Correction Function Method ??
Dongfang Li and
Mianfu She and
Xiaoqiang Yan A Novel Discrete Fractional Grönwall-Type
Inequality and Its Application in
Pointwise-in-Time Error Estimates . . . ??
Martin J. Kühn and
Carola Kruse and
Ulrich Rüde Implicitly Extrapolated Geometric
Multigrid on Disk-Like Domains for the
Gyrokinetic Poisson Equation from Fusion
Plasma Applications . . . . . . . . . . ??
Elizabeth Qian and
Jemima M. Tabeart and
Akil Narayan Model Reduction of Linear Dynamical
Systems via Balancing for Bayesian
Inference . . . . . . . . . . . . . . . ??
Nicholas Paskal and
Maria Cameron An Efficient Jet Marcher for Computing
the Quasipotential for 2D SDEs . . . . . ??
Davide Palitta and
Sanda Lefteriu An Efficient, Memory-Saving Approach for
the Loewner Framework . . . . . . . . . ??
Ulrik Skre Fjordholm and
Kjetil Olsen Lye Convergence Rates of Monotone Schemes
for Conservation Laws for Data with
Unbounded Total Variation . . . . . . . ??
Myong-Song Ho and
Ji-Song Pak and
Ju-Song Kim Neighbor-Gradient Single-Pass Method for
Solving Anisotropic Eikonal Equation . . ??
Jing Sun and
Weihua Deng and
Daxin Nie Numerical Approximations for the
Fractional Fokker--Planck Equation with
Two-Scale Diffusion . . . . . . . . . . ??
A. Faghih and
P. Mokhtary Non-linear System of Multi-order
Fractional Differential Equations:
Theoretical Analysis and a Robust
Fractional Galerkin Implementation . . . ??
A. H. Bentbib and
M. El Ghomari and
K. Jbilou An Extended-Rational Arnoldi Method for
Large Matrix Exponential Evaluations . . ??
Zheng Hong and
Zhengyin Ye and
Kun Ye A Modified TENO Scheme with Improved
Efficiency . . . . . . . . . . . . . . . ??
Andrea Natale and
Gabriele Todeschi A Mixed Finite Element Discretization of
Dynamical Optimal Transport . . . . . . ??
Yiyang Liu and
Zaiwen Wen and
Wotao Yin A Multiscale Semi-Smooth Newton Method
for Optimal Transport . . . . . . . . . ??
Shuyi Wang and
Zixu Zhou and
Dongbin Xiu Construction of discontinuity detectors
using convolutional neural networks . . ??
Francesco Marchetti and
Emma Perracchione Efficient Reduced Basis Algorithm (ERBA)
for Kernel-Based Approximation . . . . . ??
Rohit Khandelwal and
Kamana Porwal Pointwise a Posteriori Error Analysis of
a Finite Element Method for the
Signorini Problem . . . . . . . . . . . ??
Chaobao Huang and
Martin Stynes A Sharp $ \alpha $-Robust $ L^\infty
(H^1)$ Error Bound for a Time-Fractional
Allen--Cahn Problem Discretised by the
Alikhanov $ L2 - 1_\sigma $ Scheme and a
Standard FEM . . . . . . . . . . . . . . ??
Pingbing Ming and
Siqi Song A Nitsche Hybrid Multiscale Method with
Non-matching Grids . . . . . . . . . . . ??
Kaiye Zhou and
Wei Gong Error Estimates for Finite Element
Approximation of Dirichlet Boundary
Control for Stokes Equations in $
\mathbf {L}^2 (\Gamma) $ . . . . . . . . ??
Martin Campos Pinto and
Katharina Kormann and
Eric Sonnendrücker Variational Framework for
Structure-Preserving Electromagnetic
Particle-in-Cell Methods . . . . . . . . ??
Yuanyuan Kang and
Hong-lin Liao Energy Stability of BDF Methods up to
Fifth-Order for the Molecular Beam
Epitaxial Model Without Slope Selection ??
Aikaterini Aretaki and
Efthymios N. Karatzas and
Georgios Katsouleas Equal Higher Order Analysis of an
Unfitted Discontinuous Galerkin Method
for Stokes Flow Systems . . . . . . . . ??
Jiangxing Wang and
Kejia Pan and
Xiaofeng Yang Convergence Analysis of the Fully
Discrete Hybridizable Discontinuous
Galerkin Method for the Allen--Cahn
Equation Based on the Invariant Energy
Quadratization Approach . . . . . . . . ??
Abeynaya Gnanasekaran and
Eric Darve Hierarchical Orthogonal Factorization:
Sparse Least Squares Problems . . . . . ??
Todd Arbogast and
Chieh-Sen Huang and
Ming-Hsien Kuo RBF WENO Reconstructions with Adaptive
Order and Applications to Conservation
Laws . . . . . . . . . . . . . . . . . . ??
Siyang Wang and
Daniel Appelö and
Gunilla Kreiss An Energy-Based Summation-by-Parts
Finite Difference Method For the Wave
Equation in Second Order Form . . . . . ??
Yukun Li and
Shuonan Wu and
Yulong Xing Finite Element Approximations of a Class
of Nonlinear Stochastic Wave Equations
with Multiplicative Noise . . . . . . . ??
Jinhong Jia and
Hong Wang and
Xiangcheng Zheng Numerical Analysis of a Fast Finite
Element Method for a Hidden-Memory
Variable-Order Time-Fractional Diffusion
Equation . . . . . . . . . . . . . . . . ??
Lidia Aceto and
Paolo Novati Exponentially Convergent Trapezoidal
Rules to Approximate Fractional Powers
of Operators . . . . . . . . . . . . . . ??
Xiangcheng Zheng and
Hong Wang Discretization and Analysis of an
Optimal Control of a Variable-Order
Time-Fractional Diffusion Equation with
Pointwise Constraints . . . . . . . . . ??
Guanyu Zhou The Convergence Analysis of Semi- and
Fully-Discrete Projection-Decoupling
Schemes for the Generalized Newtonian
Models . . . . . . . . . . . . . . . . . ??
Xiaojun Ma and
Hongwei Liu and
Xiaoyin Li Two Optimization Approaches for Solving
Split Variational Inclusion Problems
with Applications . . . . . . . . . . . ??
Luisa D'Amore and
Emil Constantinescu and
Luisa Carracciuolo A Scalable Space-Time Domain
Decomposition Approach for Solving Large
Scale Nonlinear Regularized Inverse Ill
Posed Problems in 4D Variational Data
Assimilation . . . . . . . . . . . . . . ??
Kevin Huang and
Junyu Zhang and
Shuzhong Zhang Cubic Regularized Newton Method for the
Saddle Point Models: a Global and Local
Convergence Analysis . . . . . . . . . . ??
Jinshan Zeng and
Wotao Yin and
Ding-Xuan Zhou Moreau Envelope Augmented Lagrangian
Method for Nonconvex Optimization with
Linear Constraints . . . . . . . . . . . ??
Jianyuan Yin and
Zhen Huang and
Lei Zhang Constrained High-Index Saddle Dynamics
for the Solution Landscape with Equality
Constraints . . . . . . . . . . . . . . ??
Maximilien Germain and
Mathieu Lauri\`ere and
Xavier Warin DeepSets and Their Derivative Networks
for Solving Symmetric PDEs . . . . . . . ??
Kuk Hwan Ri and
Kuk Hyon Sonu A Numerical Construction of the
Universal Feedback Control in Problems
of Nonlinear Controls Under Disturbance ??
Daniel Lindblad and
Christian Frey and
Niklas Andersson Minimizing Aliasing in Multiple
Frequency Harmonic Balance Computations ??
Haifeng Ji An Immersed Raviart--Thomas Mixed Finite
Element Method for Elliptic Interface
Problems on Unfitted Meshes . . . . . . ??
Jia Shi and
Ruipeng Li and
Maarten V. de Hoop A Non-perturbative Approach to Computing
Seismic Normal Modes in Rotating Planets ??
Z. Safari and
G. B. Loghmani and
M. Ahmadinia Convergence Analysis of a LDG Method for
Time-Space Tempered Fractional Diffusion
Equations with Weakly Singular Solutions ??
Gabriele Ciaramella and
Tommaso Vanzan Spectral Coarse Spaces for the
Substructured Parallel Schwarz Method ??
Yafei Sun and
Shu-Lin Wu and
Yingxiang Xu Correction to: A Parallel-in-Time
Implementation of the Numerov Method for
Wave Equations . . . . . . . . . . . . . ??
Mária Lukácová-Medvid'ová and
Bangwei She and
Yuhuan Yuan Error Estimates of the Godunov Method
for the Multidimensional Compressible
Euler System . . . . . . . . . . . . . . ??
Qin Li and
Dong Sun and
Xiao Huang Nonlinear Upwind-Biased
Free-Stream-Preserving Schemes for
Compressible Euler Equations . . . . . . ??
Xiao Xu and
Guoxi Ni A Finite Volume Method for the 3D
Lagrangian Ideal Compressible
Magnetohydrodynamics . . . . . . . . . . ??
Thuy T. Le and
Loc H. Nguyen The Gradient Descent Method for the
Convexification to Solve Boundary Value
Problems of Quasi-Linear PDEs and a
Coefficient Inverse Problem . . . . . . ??
Mingcai Ding and
Xiaoliang Song and
Bo Yu An Inexact Proximal DC Algorithm with
Sieving Strategy for Rank Constrained
Least Squares Semidefinite Programming ??
Susanne C. Brenner and
José C. Garay and
Li-Yeng Sung Multiscale Finite Element Methods for an
Elliptic Optimal Control Problem with
Rough Coefficients . . . . . . . . . . . ??
Bo Lin and
Qianxiao Li and
Weiqing Ren Computing the Invariant Distribution of
Randomly Perturbed Dynamical Systems
Using Deep Learning . . . . . . . . . . ??
Ching-Sung Liu Exact and Inexact Iterative Methods for
Finding the Largest Eigenpair of a
Weakly Irreducible Nonnegative Tensor ??
Yao Xiao and
Jan Glaubitz and
Guohui Song Sequential Image Recovery from Noisy and
Under-Sampled Fourier Data . . . . . . . ??
Xianjin Chen and
Zhaoxiang Li and
Jianxin Zhou An Improved Local-Min-Orthogonal Method
for Finding Multiple Solutions to
Nonlinear Elliptic PDEs . . . . . . . . ??
Christoph Erath and
Lorenzo Mascotto and
Alexander Rieder Mortar Coupling of $ h p$-Discontinuous
Galerkin and Boundary Element Methods
for the Helmholtz Equation . . . . . . . ??
L. Fatone and
D. Funaro and
G. Manzini A Decision-Making Machine Learning
Approach in Hermite Spectral
Approximations of Partial Differential
Equations . . . . . . . . . . . . . . . ??
Taibai Fu and
Changfa Du and
Yufeng Xu An Effective Finite Element Method with
Shifted Fractional Powers Bases for
Fractional Boundary Value Problems . . . ??
Oscar Balcells-Quintana and
David Codony and
Sonia Fernández-Méndez C0-IPM with Generalised Periodicity and
Application to Flexoelectricity-Based 2D
Metamaterials . . . . . . . . . . . . . ??
Zachary J. Grant Perturbed Runge--Kutta Methods for Mixed
Precision Applications . . . . . . . . . ??
Lisang Ding and
Wuchen Li and
Wotao Yin A Mean Field Game Inverse Problem . . . ??
Yu-Bang Zheng and
Ting-Zhu Huang and
Qibin Zhao Tensor Completion via Fully-Connected
Tensor Network Decomposition with
Regularized Factors . . . . . . . . . . ??
Yue Wang and
Fuzheng Gao and
Jintao Cui A Conforming Discontinuous Galerkin
Finite Element Method for Linear
Elasticity Interface Problems . . . . . ??
Ravina Shokeen and
Ajit Patel and
Amiya K. Pani Primal Hybrid Method For Quasilinear
Parabolic Problems . . . . . . . . . . . ??
Aytura Keram and
Pengzhan Huang The Arrow-Hurwicz Iterative Finite
Element Method for the Stationary
Thermally Coupled Incompressible
Magnetohydrodynamics Flow . . . . . . . ??
Víctor Beltrán and
Soledad Le Clainche and
José M. Vega An Adaptive Data-Driven Reduced Order
Model Based on Higher Order Dynamic Mode
Decomposition . . . . . . . . . . . . . ??
Min Ling and
Weimin Han and
Shengda Zeng A Pressure Projection Stabilized Mixed
Finite Element Method for a Stokes
Hemivariational Inequality . . . . . . . ??
Xinghui Zhong and
Chi-Wang Shu Entropy Stable Galerkin Methods with
Suitable Quadrature Rules for Hyperbolic
Systems with Random Inputs . . . . . . . ??
Sehun Chun and
Taejin Oh Divergence/Connection Preservation
Scheme in the Curvilinear Domain with a
Small Geometric Approximation Error . . ??
Soobin Kwak and
Hyun Geun Lee and
Junseok Kim Motion by Mean Curvature with
Constraints Using a Modified Allen--Cahn
Equation . . . . . . . . . . . . . . . . ??
Xi Chen and
Yuwen Li Superconvergent Pseudostress-Velocity
Finite Element Methods for the Oseen
Equations . . . . . . . . . . . . . . . ??
Zi-Hang She A Class of Unconditioned Stable 4-Point
WSGD Schemes and Fast Iteration Methods
for Space Fractional Diffusion Equations ??
Marcello Longo Adaptive Quasi-Monte Carlo Finite
Element Methods for Parametric Elliptic
PDEs . . . . . . . . . . . . . . . . . . ??
Chenxi Wang and
Yichen Guo and
Zhen Zhang Unconditionally Energy Stable and
Bound-Preserving Schemes for Phase-Field
Surfactant Model with Moving Contact
Lines . . . . . . . . . . . . . . . . . ??
Yanfang Yang and
Shubin Fu and
Eric T. Chung An Adaptive Generalized Multiscale
Finite Element Method Based Two-Grid
Preconditioner for Large Scale
High-Contrast Linear Elasticity Problems ??
Guiyun Xiao and
Zheng-Jian Bai A Geometric Proximal Gradient Method for
Sparse Least Squares Regression with
Probabilistic Simplex Constraint . . . . ??
Xingjian Xu and
Minghua Chen Discovery of Subdiffusion Problem with
Noisy Data via Deep Learning . . . . . . ??
Baiju Zhang and
Hengguang Li and
Zhimin Zhang Solving Biharmonic Eigenvalue Problem
With Navier Boundary Condition Via
Poisson Solvers On Non-Convex Domains ??
Qin Zhou and
Minfu Feng Analysis of a Full Discretization for a
Fractional/Normal Diffusion Equation
with Rough Dirichlet Boundary Data . . . ??
Xuelong Gu and
Chaolong Jiang and
Wenjun Cai Efficient Energy-Preserving Exponential
Integrators for Multi-component
Hamiltonian Systems . . . . . . . . . . ??
Jinxue Fu and
Weiming Li and
Yanli Wang An Asymptotic-Preserving IMEX Method for
Nonlinear Radiative Transfer Equation ??
Lorenzo Botti and
Francesco Carlo Massa HHO Methods for the Incompressible
Navier--Stokes and the Incompressible
Euler Equations . . . . . . . . . . . . ??
Siye Li and
Zhensheng Sun and
Ding Yao A Spatio-temporal Optimal, Hybird
Compact-WENO Scheme with Minimized
Dispersion and Critical-adaptive
Dissipation for Solving Compressible
Flows . . . . . . . . . . . . . . . . . ??
Kleiton A. Schneider and
José M. Gallardo and
Cipriano Escalante Efficient GPU Implementation of
Multidimensional Incomplete Riemann
Solvers for Hyperbolic Nonconservative
Systems: Applications to Shallow Water
Systems with Topography and Dry Areas ??
Wenbin Chen and
Jianyu Jing and
Xiaoming Wang A Positivity Preserving, Energy Stable
Finite Difference Scheme for the
Flory--Huggins--Cahn--Hilliard--Navier--Stokes System ??
Tian-jun Wang A New Multi-Domain Spectral Method for
Korteweg--de Vries Equation on The Whole
Line . . . . . . . . . . . . . . . . . . ??
Qiuxiang Zhong and
Ryan Wen Liu and
Yuping Duan Spatially Adapted First and Second Order
Regularization for Image Reconstruction:
From an Image Surface Perspective . . . ??
Evangelos Galaris and
Gianluca Fabiani and
Constantinos Siettos Numerical Bifurcation Analysis of PDEs
From Lattice Boltzmann Model
Simulations: a Parsimonious Machine
Learning Approach . . . . . . . . . . . ??
Sifan Wang and
Hanwen Wang and
Paris Perdikaris Improved Architectures and Training
Algorithms for Deep Operator Networks ??
Giacomo Ascione and
Salvatore Cuomo A Sojourn-Based Approach to Semi-Markov
Reinforcement Learning . . . . . . . . . ??
Kouta Futai and
Niklas Kolbe and
Tasuku Suzuki A Mass-Preserving Two-Step
Lagrange--Galerkin Scheme for
Convection--Diffusion Problems . . . . . ??
Wim A. Mulder More Continuous Mass-Lumped Triangular
Finite Elements . . . . . . . . . . . . ??
Abram Rodgers and
Alec Dektor and
Daniele Venturi Adaptive Integration of Nonlinear
Evolution Equations on Tensor Manifolds ??
Wei-Hung Liao and
Mei-Heng Yueh A Constructive Algorithm for Disk
Conformal Parameterizations . . . . . . ??
Xin Huang and
Dongfang Li and
Hai-Wei Sun and
Fan Zhang Preconditioners with Symmetrized
Techniques for Space Fractional
Cahn--Hilliard Equations . . . . . . . . ??
Wanyou Cheng and
Xiao Wang and
Xiaojun Chen An Interior Stochastic Gradient Method
for a Class of Non--Lipschitz
Optimization Problems . . . . . . . . . ??
Yuxiang Chen and
Zhihao Ge Multiphysics Finite Element Method for
Quasi-Static Thermo-Poroelasticity . . . ??
Lina Zhao Analysis of a Mixed DG Method for
Stress--Velocity Formulation of the
Stokes Equations . . . . . . . . . . . . ??
J. W. Banks and
B. Brett Buckner and
T. Hagstrom Continuous/Discontinuous Galerkin
Difference Discretizations of High-Order
Differential Operators . . . . . . . . . ??
Yi-Shuai Niu and
Roland Glowinski Discrete Dynamical System Approaches for
Boolean Polynomial Optimization . . . . ??
Tatyana Sorokina and
Shangyou Zhang An Interpolated Galerkin Finite Element
Method for the Poisson Equation . . . . ??
Tingting Wu and
Yuesheng Xu Inverting Incomplete Fourier Transforms
by a Sparse Regularization Model and
Applications in Seismic Wavefield
Modeling . . . . . . . . . . . . . . . . ??
Qipin Chen and
Wenrui Hao Randomized Newton's Method for Solving
Differential Equations Based on the
Neural Network Discretization . . . . . ??
André L. Marchildon and
David W. Zingg Unisolvency for Polynomial Interpolation
in Simplices with Symmetrical Nodal
Distributions . . . . . . . . . . . . . ??
Aaron Baier-Reinio and
Sander Rhebergen and
Garth N. Wells Analysis of Pressure-Robust
Embedded--Hybridized Discontinuous
Galerkin Methods for the Stokes Problem
Under Minimal Regularity . . . . . . . . ??
Hong-lin Liao and
Bingquan Ji and
Lin Wang and
Zhimin Zhang Mesh-Robustness of an Energy Stable BDF2
Scheme with Variable Steps for the
Cahn--Hilliard Model . . . . . . . . . . ??
Yongyong Cai and
Xuanxuan Zhou Uniformly Accurate Nested Picard
Iterative Integrators for the
Klein--Gordon Equation in the
Nonrelativistic Regime . . . . . . . . . ??
L'ubom\'ìr Ba\vnas and
Herbert Dawid and
Tsiry Avisoa Randrianasolo and
Johannes Storn and
Xingang Wen Numerical Approximation of a System of
Hamilton--Jacobi--Bellman Equations
Arising in Innovation Dynamics . . . . . ??
G. Deugoue and
J. K. Djoko and
V. S. Konlack and
M. Mbehou Numerical Analysis of a
Darcy--Forchheimer Model Coupled with
the Heat Equation . . . . . . . . . . . ??
Jeff Calder and
Sangmin Park and
Dejan Slepcev Boundary Estimation from Point Clouds:
Algorithms, Guarantees and Applications ??
Zhaonan Dong and
Emmanuil H. Georgoulis Robust Interior Penalty Discontinuous
Galerkin Methods . . . . . . . . . . . . ??
Mofdi El-Amrani and
Abdellah El-Kacimi and
Bassou Khouya and
Mohammed Seaid Bernstein--Bézier
Galerkin-Characteristics Finite Element
Method for Convection--Diffusion
Problems . . . . . . . . . . . . . . . . ??
Xiaoxuan Yu and
Yan Xu and
Qiang Du Numerical Simulation of Singularity
Propagation Modeled by Linear Convection
Equations with Spatially Heterogeneous
Nonlocal Interactions . . . . . . . . . ??
Philipp Birken and
Viktor Linders Conservation Properties of Iterative
Methods for Implicit Discretizations of
Conservation Laws . . . . . . . . . . . ??
Zhe Ji and
Tian Liang and
Lin Fu A Class of New High-order Finite-Volume
TENO Schemes for Hyperbolic Conservation
Laws with Unstructured Meshes . . . . . ??
Björn Liljegren-Sailer and
Nicole Marheineke On Snapshot-Based Model Reduction Under
Compatibility Conditions for a Nonlinear
Flow Problem on Networks . . . . . . . . ??
Tommaso Bevilacqua and
Simone Scacchi BDDC Preconditioners for Divergence Free
Virtual Element Discretizations of the
Stokes Equations . . . . . . . . . . . . ??
Fangxiong Cheng and
Hui Xu and
Xinlong Feng Retracted Article: Model Order Reduction
Method Based on Machine Learning for
Parameterized Time-Dependent Partial
Differential Equations . . . . . . . . . ??
Yana Di and
Yifan Wei and
Jiwei Zhang and
Chengchao Zhao Sharp Error Estimate of an Implicit BDF2
Scheme with Variable Time Steps for the
Phase Field Crystal Model . . . . . . . ??
Lili Ju and
Xiao Li and
Zhonghua Qiao Stabilized Exponential--SAV Schemes
Preserving Energy Dissipation Law and
Maximum Bound Principle for The
Allen--Cahn Type Equations . . . . . . . ??
Xiangyun Meng and
Martin Stynes Balanced-Norm and Energy-Norm Error
Analyses for a Backward Euler/FEM
Solving a Singularly Perturbed Parabolic
Reaction--Diffusion Problem . . . . . . ??
Jikun Zhao and
Tianle Wang and
Bei Zhang The Stabilized Nonconforming Virtual
Element Method for Linear Elasticity
Problem . . . . . . . . . . . . . . . . ??
Yangyang Cao and
Alexander Kurganov and
Yongle Liu and
Ruixiao Xin Flux Globalization Based Well-Balanced
Path-Conservative Central-Upwind Schemes
for Shallow Water Models . . . . . . . . ??
Han Zhou and
Wenyi Tian Two Time-Stepping Schemes for
Sub-Diffusion Equations with Singular
Source Terms . . . . . . . . . . . . . . ??
Santiago Badia and
Jérôme Droniou and
Liam Yemm Conditioning of a Hybrid High-Order
Scheme on Meshes with Small Faces . . . ??
Qingshan Chen and
Lili Ju and
Roger Temam Conservative Numerical Schemes with
Optimal Dispersive Wave Relations: Part
II. Numerical Evaluations . . . . . . . ??
Qingtao Li and
Guangzhi Du Local and Parallel Finite Element
Methods Based on Two-grid
Discretizations for a Transient Coupled
Navier--Stokes/Darcy Model . . . . . . . ??
Tuan Anh Dao and
Murtazo Nazarov A High-Order Residual-Based Viscosity
Finite Element Method for the Ideal MHD
Equations . . . . . . . . . . . . . . . ??
Yu-ling Guo and
Zhong-qing Wang A Two-Grid Spectral Deferred Correction
Method for the Multi-Order Fractional
Differential Equations . . . . . . . . . ??
Zhongjie Lu and
Yan Xu A Parallel Eigensolver for Photonic
Crystals Discretized by Edge Finite
Elements . . . . . . . . . . . . . . . . ??
Huan Ren and
Ru-Ru Ma and
Qiaohua Liu and
Zheng-Jian Bai Randomized Quaternion QLP Decomposition
for Low-Rank Approximation . . . . . . . ??
Gustav Eriksson and
Ken Mattsson Weak Versus Strong Wall Boundary
Conditions for the Incompressible
Navier--Stokes Equations . . . . . . . . ??
Hongpeng Sun An Investigation on Semismooth Newton
based Augmented Lagrangian Method for
Image Restoration . . . . . . . . . . . ??
Ben-Zheng Li and
Xi-Le Zhao and
Teng-Yu Ji and
Xiong-Jun Zhang and
Ting-Zhu Huang Nonlinear Transform Induced Tensor
Nuclear Norm for Tensor Completion . . . ??
A. F. Hegarty and
E. O'Riordan A Numerical Method for Singularly
Perturbed Convection-diffusion Problems
Posed on Smooth Domains . . . . . . . . ??
Fei Xu and
Qiumei Huang and
Haishen Dai and
Hongkun Ma Multilevel Local Defect-Correction
Method for Nonsymmetric Eigenvalue
Problems . . . . . . . . . . . . . . . . ??
Guosheng Fu A High-Order Velocity-Based
Discontinuous Galerkin Scheme for the
Shallow Water Equations: Local
Conservation, Entropy Stability,
Well-Balanced Property, and Positivity
Preservation . . . . . . . . . . . . . . ??
Tristan Montoya and
David W. Zingg A Unifying Algebraic Framework for
Discontinuous Galerkin and Flux
Reconstruction Methods Based on the
Summation-by-Parts Property . . . . . . ??
Salvatore Cuomo and
Vincenzo Schiano Di Cola and
Fabio Giampaolo and
Gianluigi Rozza and
Maziar Raissi and
Francesco Piccialli Scientific Machine Learning Through
Physics-Informed Neural Networks: Where
we are and What's Next . . . . . . . . . ??
Yuping Duan and
Qiuxiang Zhong and
Xue-Cheng Tai and
Roland Glowinski A Fast Operator-splitting Method for
Beltrami Color Image Denoising . . . . . ??
Li Wang and
Ming Yan Hessian Informed Mirror Descent . . . . ??
Wei Gong and
Buyang Li and
Huanhuan Yang Optimal Control in a Bounded Domain for
Wave Propagating in the Whole Space:
Coupling Through Boundary Integral
Equations . . . . . . . . . . . . . . . ??
N. A. Barnafi and
B. Gómez-Vargas and
W. J. Lourenço and
R. F. Reis and
B. M. Rocha and
M. Lobosco and
R. Ruiz-Baier and
R. Weber dos Santos Finite Element Methods for Large-Strain
Poroelasticity/Chemotaxis Models
Simulating the Formation of Myocardial
Oedema . . . . . . . . . . . . . . . . . ??
Maolin Che and
Yimin Wei An Efficient Algorithm for Computing the
Approximate $t$-URV and its Applications ??
Minghan Yang and
Dong Xu and
Zaiwen Wen and
Mengyun Chen and
Pengxiang Xu Sketch-Based Empirical Natural Gradient
Methods for Deep Learning . . . . . . . ??
Jun Guo and
Minfu Feng A Robust and Mass Conservative Virtual
Element Method for Linear Three-field
Poroelasticity . . . . . . . . . . . . . ??
Luca Desiderio and
Silvia Falletta and
Matteo Ferrari and
Letizia Scuderi CVEM-BEM Coupling with Decoupled Orders
for 2D Exterior Poisson Problems . . . . ??
Zhaohui Fu and
Tao Tang and
Jiang Yang Energy Plus Maximum Bound Preserving
Runge--Kutta Methods for the Allen--Cahn
Equation . . . . . . . . . . . . . . . . ??
Tan Tan and
Wei-Ping Bu and
Ai-Guo Xiao L1 Method on Nonuniform Meshes for
Linear Time-Fractional Diffusion
Equations with Constant Time Delay . . . ??
Yanping Chen and
Lina Wang and
Lijun Yi Exponential Convergence of
hp-discontinuous Galerkin Method for
Nonlinear Caputo Fractional Differential
Equations . . . . . . . . . . . . . . . ??
Stefano Berrone and
Claudio Canuto and
Moreno Pintore Variational Physics Informed Neural
Networks: the Role of Quadratures and
Test Functions . . . . . . . . . . . . . ??
Y. Rong and
J. A. Fiordilino and
F. Shi and
Y. Cao A Modular Voigt Regularization of the
Crank--Nicolson Finite Element Method
for the Navier--Stokes Equations . . . . ??
Manuel Quezada de Luna and
David I. Ketcheson Maximum Principle Preserving Space and
Time Flux Limiting for Diagonally
Implicit Runge--Kutta Discretizations of
Scalar Convection--Diffusion Equations ??
Gabriel N. Gatica and
Cristian Inzunza and
Filánder A. Sequeira A Pseudostress-Based Mixed-Primal Finite
Element Method for Stress-Assisted
Diffusion Problems in Banach Spaces . . ??
Xiaoli Lu and
Pengzhan Huang and
Xinlong Feng and
Yinnian He A Stabilized Difference Finite Element
Method for the 3D Steady Incompressible
Navier--Stokes Equations . . . . . . . . ??
Guangwei Gao and
Shuonan Wu Auxiliary Space Preconditioners for a $
C^0 $ Finite Element Approximation of
Hamilton--Jacobi--Bellman Equations with
Cordes Coefficients . . . . . . . . . . ??
Yuchao Tang and
Meng Wen and
Tieyong Zeng Preconditioned Three-Operator Splitting
Algorithm with Applications to Image
Restoration . . . . . . . . . . . . . . ??
Lexing Ying Pole Recovery From Noisy Data on
Imaginary Axis . . . . . . . . . . . . . ??
Xihui Xie On Adaptive Grad--Div Parameter
Selection . . . . . . . . . . . . . . . ??
Yong Liu and
Jianfang Lu and
Qi Tao and
Yinhua Xia An Oscillation-free Discontinuous
Galerkin Method for Shallow Water
Equations . . . . . . . . . . . . . . . ??
Bingkun Wang and
Lei Liu and
Yuchong Li and
Mohammad Khishe Robust Grey Wolf Optimizer for
Multimodal Optimizations: a
Cross-Dimensional Coordination Approach ??
Xu Qian and
Jian Dong and
Songhe Song Positivity-Preserving and Well-Balanced
Adaptive Surface Reconstruction Schemes
for Shallow Water Equations with
Wet--Dry Fronts . . . . . . . . . . . . ??
Wen Huang and
Kyle A. Gallivan A Limited-Memory Riemannian Symmetric
Rank-One Trust-Region Method with a
Restart Strategy . . . . . . . . . . . . ??
Baochen Sun and
Huibin Chang Proximal Gradient Methods for General
Smooth Graph Total Variation Model in
Unsupervised Learning . . . . . . . . . ??
Yupeng Ren and
Yulong Xing and
Dean Wang and
Jianxian Qiu High Order Asymptotic Preserving Hermite
WENO Fast Sweeping Method for the
Steady-State $ S_N $ Transport Equations ??
Yue Wang and
Xiangyun Meng and
Yonghai Li The Bogner--Fox--Schmit Element Finite
Volume Methods on the Shishkin Mesh for
Fourth-Order Singularly Perturbed
Elliptic Problems . . . . . . . . . . . ??
Jian Li and
Jing Yue and
Wen Zhang and
Wansuo Duan The Deep Learning Galerkin Method for
the General Stokes Equations . . . . . . ??
Luis Ángel Larios-Cárdenas and
Frédéric Gibou Error-Correcting Neural Networks for
Two-Dimensional Curvature Computation in
the Level-set Method . . . . . . . . . . ??
Tianhang Liu and
Yimin Wei The Abstract Laplacian Tensor of a
Hypergraph with Applications in
Clustering . . . . . . . . . . . . . . . ??
Mariam Al-Maskari and
Samir Karaa Error Estimates for Approximations of
Time-Fractional Biharmonic Equation with
Nonsmooth Data . . . . . . . . . . . . . ??
Tingting Wu and
Zhihui Mao and
Zeyu Li and
Yonghua Zeng and
Tieyong Zeng Efficient Color Image Segmentation via
Quaternion-based $ L_1 $ /$ L_2 $
Regularization . . . . . . . . . . . . . ??
Felipe Lepe and
Gonzalo Rivera and
Jesus Vellojin A Posteriori Analysis for a Mixed FEM
Discretization of the Linear Elasticity
Spectral Problem . . . . . . . . . . . . ??
Argyrios Petras and
Leevan Ling and
Steven J. Ruuth Meshfree Semi-Lagrangian Methods for
Solving Surface Advection PDEs . . . . . ??
Shuhao Cao and
Long Chen and
Ruchi Guo and
Frank Lin Immersed Virtual Element Methods for
Elliptic Interface Problems in Two
Dimensions . . . . . . . . . . . . . . . ??
Qi Tao and
Liangyue Ji and
Jennifer K. Ryan and
Yan Xu Accuracy-Enhancement of Discontinuous
Galerkin Methods for PDEs Containing
High Order Spatial Derivatives . . . . . ??
Xiaotao Zhang and
Tiegang Liu and
Changsheng Yu and
Chengliang Feng and
Zhiqiang Zeng and
Kun Wang A Second-order Modified Ghost Fluid
Method (2nd-MGFM) with Discontinuous
Galerkin Method for $1$-D compressible
Multi-medium Problem with Cylindrical
and Spherical Symmetry . . . . . . . . . ??
Alexandre Caboussat and
Roland Glowinski and
Dimitrios Gourzoulidis A Least-Squares Method for the Solution
of the Non-smooth Prescribed Jacobian
Equation . . . . . . . . . . . . . . . . ??
Jiachuan Zhang and
Ran Zhang and
Xiaoshen Wang A Posteriori Estimates of Taylor--Hood
Element for Stokes Problem Using
Auxiliary Subspace Techniques . . . . . ??
Brittany A. Erickson and
Jeremy E. Kozdon and
Tobias Harvey A Non-Stiff Summation-By-Parts Finite
Difference Method for the Scalar Wave
Equation in Second Order Form:
Characteristic Boundary Conditions and
Nonlinear Interfaces . . . . . . . . . . ??
Konstantin Avrachenkov and
Patrick Brown and
Nelly Litvak Red Light Green Light Method for Solving
Large Markov Chains . . . . . . . . . . ??
Qigang Liang and
Xuejun Xu and
Liuyao Yuan A Weak Galerkin Finite Element Method
Can Compute Both Upper and Lower
Eigenvalue Bounds . . . . . . . . . . . ??
Wei Wu and
Xinlong Feng and
Hui Xu Improved Deep Neural Networks with
Domain Decomposition in Solving Partial
Differential Equations . . . . . . . . . ??
Hongqiang Zhu and
Zhihuan Wang and
Haiyun Wang and
Qiang Zhang and
Zhen Gao Troubled-Cell Indication Using $K$-means
Clustering with Unified Parameters . . . ??
Yabing Sun and
Quan Zhou Error Estimate of Exponential Time
Differencing Runge--Kutta Scheme for the
Epitaxial Growth Model Without Slope
Selection . . . . . . . . . . . . . . . ??
Shinhoo Kang and
Emil M. Constantinescu Entropy-Preserving and Entropy-Stable
Relaxation IMEX and Multirate
Time-Stepping Methods . . . . . . . . . ??
Olaniyi S. Iyiola and
Yekini Shehu Inertial Version of Generalized
Projected Reflected Gradient Method . . ??
Fengshan Zhang and
Yongkui Zou and
Shimin Chai and
Ran Zhang and
Yanzhao Cao Splitting-up Spectral Method for
Nonlinear Filtering Problems with
Correlation Noises . . . . . . . . . . . ??
N Shravani and
G Murali Mohan Reddy and
A. K. Pani Anisotropic \em a Posteriori Error
Analysis for the Two-Step Backward
Differentiation Formula for Parabolic
Integro--Differential Equation . . . . . ??
Clément Rudel and
Sébastien Pernet and
Jean-Philippe Brazier Numerical Factorization of Propagation
Operator for Hyperbolic Equations and
Application to One-way, True Amplitude
One-way Equations and Bremmer Series . . ??
Wenjia Liu and
Shuo Zhang A Lowest-Degree Conservative Finite
Element Scheme for Incompressible Stokes
Problems on General Triangulations . . . ??
Wenbin Dong and
Yingjie Liu and
Hansong Tang Accuracy Enhancing Interface Treatment
Algorithm: The Back and Forth Error
Compensation and Correction Method . . . ??
Shaolin Ji and
Shige Peng and
Ying Peng and
Xichuan Zhang Solving Stochastic Optimal Control
Problem via Stochastic Maximum Principle
with Deep Learning Method . . . . . . . ??
Jiankang Shi and
Minghua Chen and
Yubin Yan and
Jianxiong Cao Correction of High-Order $ L_k $
Approximation for Subdiffusion . . . . . ??
Yang Xu and
Zhenguo Zhou and
Jingjun Zhao Conforming Virtual Element Methods for
Sobolev Equations . . . . . . . . . . . ??
Hong Zhang and
Zhengyu Liu and
Emil Constantinescu and
Robert Jacob Stability Analysis of Coupled
Advection--Diffusion Models with Bulk
Interface Condition . . . . . . . . . . ??
Pin Lyu and
Seakweng Vong A Symmetric Fractional-order Reduction
Method for Direct Nonuniform
Approximations of Semilinear
Diffusion-wave Equations . . . . . . . . ??
S. R. Siva Prasad Kochi and
M. Ramakrishna A Discontinuous Galerkin Overset Scheme
Using WENO Reconstruction and Subcells
for Two-Dimensional Problems . . . . . . ??
David A. Craig Penner and
David W. Zingg Accurate High-Order Tensor-Product
Generalized Summation-By-Parts
Discretizations of Hyperbolic
Conservation Laws: General Curved
Domains and Functional Superconvergence ??
Zhengjie Sun and
Wenwu Gao and
Ran Yang A Convergent Iterated
Quasi-interpolation for Periodic Domain
and Its Applications to Surface PDEs . . ??
Tao Tang and
Xu Wu and
Jiang Yang Arbitrarily High Order and Fully
Discrete Extrapolated RK-SAV/DG Schemes
for Phase-field Gradient Flows . . . . . ??
Yaping Li and
Weidong Zhao and
Wenju Zhao Optimal Convergence of the Scalar
Auxiliary Variable Finite Element Method
for the Natural Convection Equations . . ??
Zixuan Gao and
Jiuyang Liang and
Zhenli Xu A Kernel-Independent Sum-of-Exponentials
Method . . . . . . . . . . . . . . . . . ??
Jinzhi Huang and
Zhongxiao Jia Two Harmonic Jacobi--Davidson Methods
for Computing a Partial Generalized
Singular Value Decomposition of a Large
Matrix Pair . . . . . . . . . . . . . . ??
T. M. Cavalcante and
R. J. M. Lira Filho and
A. C. R. Souza and
D. K. E. Carvalho and
P. R. M. Lyra A Multipoint Flux Approximation with a
Diamond Stencil and a Non-Linear Defect
Correction Strategy for the Numerical
Solution of Steady State Diffusion
Problems in Heterogeneous and
Anisotropic Media Satisfying the
Discrete Maximum Principle . . . . . . . ??
Lin Fu and
Tian Liang A New Adaptation Strategy for
Multi-resolution Method . . . . . . . . ??
Jun Liu and
Hongfei Fu An Efficient QSC Approximation of
Variable-Order Time-Fractional
Mobile--Immobile Diffusion Equations
with Variably Diffusive Coefficients . . ??
Tao Sun and
Zhi Wang and
Hai-Wei Sun and
Chengjian Zhang A Sixth-Order Quasi-Compact Difference
Scheme for Multidimensional Poisson
Equations Without Derivatives of Source
Term . . . . . . . . . . . . . . . . . . ??
Lingling Zhou and
Ruihan Guo Optimal Error Estimates of the Local
Discontinuous Galerkin Method and
High-order Time Discretization Scheme
for the Swift--Hohenberg Equation . . . ??
Hongjin He and
Chen Ling and
Wenhui Xie Tensor Completion via A Generalized
Transformed Tensor T-Product
Decomposition Without t-SVD . . . . . . ??
G. Sáez-Mischlich and
J. Sierra-Ausín and
J. Gressier The Spectral Difference Raviart--Thomas
Method for Two and Three-Dimensional
Elements and Its Connection with the
Flux Reconstruction Formulation . . . . ??
Cheng-Yao Lyu and
Xi-Le Zhao and
Ben-Zheng Li and
Hao Zhang and
Ting-Zhu Huang Multi-Dimensional Image Recovery via
Fully-Connected Tensor Network
Decomposition Under the Learnable
Transforms . . . . . . . . . . . . . . . ??
Sergio Caucao and
Gabriel N. Gatica and
Ricardo Oyarzúa and
Paulo Zúñiga A Posteriori Error Analysis of a Mixed
Finite Element Method for the Coupled
Brinkman--Forchheimer and
Double-Diffusion Equations . . . . . . . ??
Na Gong and
Wanshan Li High-Order ADI--FDTD Schemes for
Maxwell's Equations with Material
Interfaces in Two Dimensions . . . . . . ??
Ruyu Wang and
Chao Zhang and
Lichun Wang and
Yuanhai Shao A Stochastic Nesterov's Smoothing
Accelerated Method for General Nonsmooth
Constrained Stochastic Composite Convex
Optimization . . . . . . . . . . . . . . ??
Shimin Guo and
Wenjing Yan and
Can Li and
Liquan Mei Dissipation-Preserving Rational
Spectral-Galerkin Method for Strongly
Damped Nonlinear Wave System Involving
Mixed Fractional Laplacians in Unbounded
Domains . . . . . . . . . . . . . . . . ??
Birgul Koc and
Changhong Mou and
Honghu Liu and
Zhu Wang and
Gianluigi Rozza and
Traian Iliescu Verifiability of the Data-Driven
Variational Multiscale Reduced Order
Model . . . . . . . . . . . . . . . . . ??
Wansheng Wang and
Mengli Mao and
Yi Huang A Posteriori Error Control and
Adaptivity for the IMEX BDF2 Method for
PIDEs with Application to Options
Pricing Models . . . . . . . . . . . . . ??
Saray Busto and
Michael Dumbser A New Family of Thermodynamically
Compatible Discontinuous Galerkin
Methods for Continuum Mechanics and
Turbulent Shallow Water Flows . . . . . ??
Ludovica Cicci and
Stefania Fresca and
Andrea Manzoni Deep-HyROMnet: a Deep Learning-Based
Operator Approximation for
Hyper-Reduction of Nonlinear
Parametrized PDEs . . . . . . . . . . . ??
Duy Phan and
Alexander Ostermann Exponential Integrators for Second-Order
in Time Partial Differential Equations ??
Marius Paul Bruchhäuser and
Uwe Köcher and
Markus Bause On the Implementation of an Adaptive
Multirate Framework for Coupled
Transport and Flow . . . . . . . . . . . ??
Rooholah Abedian and
Mehdi Dehghan A RBF--WENO Finite Difference Scheme for
Non-linear Degenerate Parabolic
Equations . . . . . . . . . . . . . . . ??
Shan-Qi Duan and
Xue-Feng Duan and
Xi-Le Zhao A New Tensor Multi-rank Approximation
with Total Variation Regularization for
Tensor Completion . . . . . . . . . . . ??
N. K. Chada and
H. Hoel and
A. Jasra and
G. E. Zouraris Improved Efficiency of Multilevel Monte
Carlo for Stochastic PDE through Strong
Pairwise Coupling . . . . . . . . . . . ??
Weiguo Gao and
Yingzhou Li and
Bichen Lu Triangularized Orthogonalization-Free
Method for Solving Extreme Eigenvalue
Problems . . . . . . . . . . . . . . . . ??
Xi Li and
Yan Luo and
Minfu Feng An Efficient Chorin--Temam Projection
Proper Orthogonal Decomposition Based
Reduced-Order Model for Nonstationary
Stokes Equations . . . . . . . . . . . . ??
Yidu Yang and
Shixi Wang and
Hai Bi The Finite Element Method for the
Elastic Transmission Eigenvalue Problem
with Different Elastic Tensors . . . . . ??
Yu Li and
Manting Xie and
Chunguang Xiong A New Family of Mixed Method for the
Biharmonic Eigenvalue Problem Based on
the First Order Equations of
Hellan--Herrmann--Johnson Type . . . . . ??
Ashley Prater-Bennette and
Lixin Shen and
Erin E. Tripp The Proximity Operator of the Log--Sum
Penalty . . . . . . . . . . . . . . . . ??
Daniel H. Baffet and
Yannik G. Gleichmann and
Marcus J. Grote Error Estimates for Adaptive Spectral
Decompositions . . . . . . . . . . . . . ??
Chao Wu and
Yunqing Huang and
Nianyu Yi and
Huayi Wei and
Jinyun Yuan Function and Curl Recovery for the
Lowest Order Triangular Edge Element . . ??
Xiaokai Chang and
Junfeng Yang GRPDA Revisited: Relaxed Condition and
Connection to Chambolle--Pock's
Primal--Dual Algorithm . . . . . . . . . ??
Fangxiong Cheng and
Xu Hui and
Xinlong Feng Retraction Note to: Model Order
Reduction Method Based on Machine
Learning for Parameterized
Time-Dependent Partial Differential
Equations . . . . . . . . . . . . . . . ??
Jun Zhu and
Jianxian Qiu A Finite Difference Mapped WENO Scheme
with Unequal-Size Stencils for
Hyperbolic Conservation Laws . . . . . . ??
Zhizhang Wu and
Zhiwen Zhang Convergence Analysis of the Localized
Orthogonal Decomposition Method for the
Semiclassical Schrödinger Equations with
Multiscale Potentials . . . . . . . . . ??
Songting Luo and
Qing Huo Liu A Fixed-Point Iteration Method for High
Frequency Helmholtz Equations . . . . . ??
Fanyi Yang and
Xiaoping Xie An Unfitted Finite Element Method by
Direct Extension for Elliptic Problems
on Domains with Curved Boundaries and
Interfaces . . . . . . . . . . . . . . . ??
Lena Leitenmaier and
Olof Runborg Heterogeneous Multiscale Methods for the
Landau--Lifshitz Equation . . . . . . . ??
Qingguo Hong and
Johannes Kraus and
Miroslav Kuchta and
Maria Lymbery and
Kent-André Mardal and
Marie E. Rognes Robust Approximation of Generalized
Biot--Brinkman Problems . . . . . . . . ??
Shuting Gu and
Hongqiao Wang and
Xiang Zhou Active Learning for Saddle Point
Calculation . . . . . . . . . . . . . . ??
Huoyuan Duan and
Qiuyu Zhang Residual-Based a Posteriori Error
Estimates for the Time-Dependent
Ginzburg--Landau Equations of
Superconductivity . . . . . . . . . . . ??
Zhen Lei and
Lei Shi and
Chenyu Zeng Solving Parametric Partial Differential
Equations with Deep Rectified Quadratic
Unit Neural Networks . . . . . . . . . . ??
Lai Wang and
Will Trojak and
Freddie Witherden and
Antony Jameson Nonlinear $p$-Multigrid Preconditioner
for Implicit Time Integration of
Compressible Navier--Stokes Equations
with $p$-Adaptive Flux Reconstruction ??
Viktor Linders On an Eigenvalue Property of
Summation-By-Parts Operators . . . . . . ??
Ferdinand Thein and
Evgeniy Romenski and
Michael Dumbser Exact and Numerical Solutions of the
Riemann Problem for a Conservative Model
of Compressible Two-Phase Flows . . . . ??
Yinghua Wang and
Bao-Shan Wang and
Leevan Ling and
Wai Sun Don A Time-Continuous Embedding Method for
Scalar Hyperbolic Conservation Laws on
Manifolds . . . . . . . . . . . . . . . ??
Huoyuan Duan and
Can Wang and
Zhijie Du A Div FOSLS Method Suitable for
Quadrilateral RT and Hexahedral RTN $
H({\rm div}) $-elements . . . . . . . . ??
Meng Li Cut-Off Error Splitting Technique for
Conservative Nonconforming VEM for
$N$-Coupled Nonlinear
Schrödinger--Boussinesq Equations . . . . ??
Huayan Zhang and
Zhichao Peng Total Generalized Variation for
Triangulated Surface Data . . . . . . . ??
Zhuo-Heng He and
Xiang-Xiang Wang and
Yun-Fan Zhao Eigenvalues of Quaternion Tensors with
Applications to Color Video Processing ??
Anthony Gruber and
Max Gunzburger and
Lili Ju and
Zhu Wang A Multifidelity Monte Carlo Method for
Realistic Computational Budgets . . . . ??
Jinzhi Huang and
Zhongxiao Jia A Cross-Product Free Jacobi--Davidson
Type Method for Computing a Partial
Generalized Singular Value Decomposition
of a Large Matrix Pair . . . . . . . . . ??
Monica Nonino and
Francesco Ballarin and
Gianluigi Rozza and
Yvon Maday Projection Based Semi-Implicit
Partitioned Reduced Basis Method for
Fluid-Structure Interaction Problems . . ??
Qile Yan and
Shixiao W. Jiang and
John Harlim Kernel-Based Methods for Solving
Time-Dependent Advection--Diffusion
Equations on Manifolds . . . . . . . . . ??
Chao Zeng Rank Properties and Computational
Methods for Orthogonal Tensor
Decompositions . . . . . . . . . . . . . ??
Juntao Huang and
Yingda Cheng and
Andrew J. Christlieb and
Luke F. Roberts Machine Learning Moment Closure Models
for the Radiative Transfer Equation III:
Enforcing Hyperbolicity and Physical
Characteristic Speeds . . . . . . . . . ??
Raffaele Marino and
Nicolas Macris Solving Non-linear Kolmogorov Equations
in Large Dimensions by Using Deep
Learning: a Numerical Comparison of
Discretization Schemes . . . . . . . . . ??
Yanli Wang and
Jie Xu $Q$-Tensor Gradient Flow with
Quasi-Entropy and Discretizations
Preserving Physical Constraints . . . . ??
Xu Yin and
Waixiang Cao A Class of Efficient Hamiltonian
Conservative Spectral Methods for
Korteweg--de Vries Equations . . . . . . ??
Sibo Cheng and
Jianhua Chen and
Charitos Anastasiou and
Panagiota Angeli and
Omar K. Matar and
Yi-Ke Guo and
Christopher C. Pain and
Rossella Arcucci Generalised Latent Assimilation in
Heterogeneous Reduced Spaces with
Machine Learning Surrogate Models . . . ??
Jiawang Nie and
Liu Yang and
Suhan Zhong and
Guangming Zhou Distributionally Robust Optimization
with Moment Ambiguity Sets . . . . . . . ??
Yahong Xiang and
Can Huang and
Huangxin Chen Optimal Convergence Analysis of a Fully
Discrete Scheme for the Stochastic
Stokes--Darcy Equations . . . . . . . . ??
Igor Tominec and
Murtazo Nazarov Residual Viscosity Stabilized RBF--FD
Methods for Solving Nonlinear
Conservation Laws . . . . . . . . . . . ??
Peng Li and
Tingting Li and
Wai-Sun Don and
Bao-Shan Wang Scale-Invariant Multi-resolution
Alternative WENO Scheme for the Euler
Equations . . . . . . . . . . . . . . . ??
Ren Liu and
Fengmiao Bian and
Xiaoqun Zhang Binary Quantized Network Training With
Sharpness-Aware Minimization . . . . . . ??
Nan Jiang and
Huanhuan Yang Fast and Accurate Artificial
Compressibility Ensemble Algorithms for
Computing Parameterized Stokes--Darcy
Flow Ensembles . . . . . . . . . . . . . ??
Johnathon Upperman and
Nail K. Yamaleev First-Order Positivity-Preserving
Entropy Stable Scheme for the $3$-D
Compressible Navier--Stokes Equations ??
Ji Li Solving Blind Ptychography Effectively
Via Linearized Alternating Direction
Method of Multipliers . . . . . . . . . ??
Han Zhou and
Wenjun Ying A Dimension Splitting Method for Time
Dependent PDEs on Irregular Domains . . ??
Songyao Duan and
Haijun Wu Adaptive FEM for Helmholtz Equation with
Large Wavenumber . . . . . . . . . . . . ??
Min Zhong and
Quoc Thong Le Gia and
Ian Hugh Sloan A Multiscale RBF Method for Severely
Ill-Posed Problems on Spheres . . . . . ??
Giorgia Franchini and
Federica Porta and
Valeria Ruggiero and
Ilaria Trombini A Line Search Based Proximal Stochastic
Gradient Algorithm with Dynamical
Variance Reduction . . . . . . . . . . . ??
Simone Chiocchetti and
Michael Dumbser An Exactly Curl-Free Staggered
Semi-Implicit Finite Volume Scheme for a
First Order Hyperbolic Model of Viscous
Two-Phase Flows with Surface Tension . . ??
Vinicius L. S. Silva and
Claire E. Heaney and
Yaqi Li and
Christopher C. Pain Data Assimilation Predictive GAN
(DA-PredGAN) Applied to a
Spatio-Temporal Compartmental Model in
Epidemiology . . . . . . . . . . . . . . ??
Sanghyun Lee and
Son-Young Yi Locking-Free and Locally-Conservative
Enriched Galerkin Method for
Poroelasticity . . . . . . . . . . . . . ??
Daniele Corallo and
Willy Dörfler and
Christian Wieners Space-Time Discontinuous Galerkin
Methods for Weak Solutions of Hyperbolic
Linear Symmetric Friedrichs Systems . . ??
Ki Wai Fong and
Shingyu Leung Spherical Essentially Non-oscillatory
(SENO) Interpolation . . . . . . . . . . ??
Hongchao Kang and
Hong Wang An Efficient Quadrature Rule for the
Oscillatory Infinite Generalized Bessel
Transform with a General Oscillator and
Its Error Analysis . . . . . . . . . . . ??
Qinghe Wang and
Mingyang Pan and
Yu-Hau Tseng and
Dongdong He An Energy Stable Immersed Boundary
Method for Deformable Membrane Problem
with Non-uniform Density and Viscosity ??
Mingzhu Zhang and
Lijun Yi Superconvergent Postprocessing of the
Continuous Galerkin Time Stepping Method
for Nonlinear Initial Value Problems
with Application to Parabolic Problems ??
Gengen Zhang and
Chaolong Jiang and
Hao Huang Arbitrarily High-Order Energy-Preserving
Schemes for the Zakharov--Rubenchik
Equations . . . . . . . . . . . . . . . ??
Yue Yu and
Jiansong Zhang and
Rong Qin The Exponential SAV Approach for the
Time-Fractional Allen--Cahn and
Cahn--Hilliard Phase-Field Models . . . ??
Haikun Dang and
Hehu Xie and
Gang Zhao and
Chenguang Zhou A Nonnested Augmented Subspace Method
for Elliptic Eigenvalue Problems with
Curved Interfaces . . . . . . . . . . . ??
Wei-Wei Xu and
Michael K. Ng A New Matrix Maximization Model for
Computing Ratios of Generalized Singular
Values from High-Order GSVD . . . . . . ??
Massimiliano Lupo Pasini and
Simona Perotto Hierarchical Model Reduction Driven by
Machine Learning for Parametric
Advection--Diffusion--Reaction Problems
in the Presence of Noisy Data . . . . . ??
Hehu Xie and
Manting Xie and
Xiaobo Yin and
Gang Zhao An Efficient Adaptive Mesh
Redistribution Method for Nonlinear
Eigenvalue Problems in Bose--Einstein
Condensates . . . . . . . . . . . . . . ??
Pierfrancesco Siena and
Michele Girfoglio and
Francesco Ballarin and
Gianluigi Rozza Data-Driven Reduced Order Modelling for
Patient-Specific Hemodynamics of
Coronary Artery Bypass Grafts with
Physical and Geometrical Parameters . . ??
Dianming Hou and
Zhonghua Qiao An Implicit--Explicit Second-Order BDF
Numerical Scheme with Variable Steps for
Gradient Flows . . . . . . . . . . . . . ??
Haikun Dang and
Yifan Wang and
Hehu Xie and
Chenguang Zhou Enhanced Error Estimates for Augmented
Subspace Method . . . . . . . . . . . . ??
John Carter and
Daozhi Han and
Nan Jiang Second Order, Unconditionally Stable,
Linear Ensemble Algorithms for the
Magnetohydrodynamics Equations . . . . . ??
Fei Xu and
Manting Xie and
Meiling Yue Multigrid Method for Nonlinear
Eigenvalue Problems Based on Newton
Iteration . . . . . . . . . . . . . . . ??
Yoshitaka Watanabe and
Takehiko Kinoshita and
Mitsuhiro T. Nakao Efficient Approaches for Verifying the
Existence and Bound of Inverse of Linear
Operators in Hilbert Spaces . . . . . . ??
Yue Li and
Lin Fu and
Nikolaus A. Adams A Family of Fast Multi-resolution ENO
Schemes for Compressible Flows . . . . . ??
Paul Novello and
Gaël Poëtte and
David Lugato and
Pietro Marco Congedo Goal-Oriented Sensitivity Analysis of
Hyperparameters in Deep Learning . . . . ??
Yiqi Gu and
Jie Shen A Fictitious Domain Spectral Method for
Solving the Helmholtz Equation in
Exterior Domains . . . . . . . . . . . . ??
Shipeng Mao and
Wendong Xue Convergence and Error Estimates of a
Mixed Discontinuous Galerkin-Finite
Element Method for the Semi-stationary
Compressible Stokes System . . . . . . . ??
L. Freret and
C. N. Ngigi and
T. B. Nguyen and
H. De Sterck and
C. P. T. Groth High-Order CENO Finite-Volume Scheme
with Anisotropic Adaptive Mesh
Refinement: Efficient Inexact Newton
Method for Steady Three-Dimensional
Flows . . . . . . . . . . . . . . . . . ??
Sixtine Michel and
Davide Torlo and
Mario Ricchiuto and
Rémi Abgrall Spectral Analysis of High Order
Continuous FEM for Hyperbolic PDEs on
Triangular Meshes: Influence of
Approximation, Stabilization, and
Time-Stepping . . . . . . . . . . . . . ??
Lingzhi Qian and
Chunya Wu and
Huiping Cai and
Xinlong Feng and
Yuanyang Qiao A Fully-Decoupled Artificial
Compressible Crank--Nicolson-Leapfrog
Time Stepping Scheme for the Phase Field
Model of Two-Phase Incompressible Flows ??
Jiani Wang and
Xiao Wang and
Liwei Zhang Stochastic Regularized Newton Methods
for Nonlinear Equations . . . . . . . . ??
Haitao Leng A Posteriori Error Analysis for
Pressure-Robust HDG Methods for the
Stationary Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . ??
Shuixin Fang and
Weidong Zhao and
Tao Zhou Strong Stability Preserving Multistep
Schemes for Forward Backward Stochastic
Differential Equations . . . . . . . . . ??
Donna Calhoun and
Erik Chudzik and
Christiane Helzel The Cartesian Grid Active Flux Method
with Adaptive Mesh Refinement . . . . . ??
Haruka Tomobe and
Vikas Sharma and
Harusato Kimura and
Hitoshi Morikawa An Energy-based Overset Finite Element
Method for Pseudo-static Structural
Analysis . . . . . . . . . . . . . . . . ??
Jian Meng and
Lourenço Beirão da Veiga and
Lorenzo Mascotto Stability and Interpolation Properties
for Stokes-Like Virtual Element Spaces ??
Shi Jin and
Zheng Ma and
Keke Wu Asymptotic-Preserving Neural Networks
for Multiscale Time-Dependent Linear
Transport Equations . . . . . . . . . . ??
Chang Liu and
William Henshaw Multigrid with Nonstandard Coarse-Level
Operators and Coarsening Factors . . . . ??
Mario J. Bencomo and
Jesse Chan Discrete Adjoint Computations for
Relaxation Runge--Kutta Methods . . . . ??
Yumin Ma and
Xingju Cai and
Bo Jiang and
Deren Han Understanding the Convergence of the
Preconditioned PDHG Method: a View of
Indefinite Proximal ADMM . . . . . . . . ??
Yihui Han and
Xiao-Ping Wang and
Xiaoping Xie An Interface/Boundary-Unfitted EXtended
HDG Method for Linear Elasticity
Problems . . . . . . . . . . . . . . . . ??
Shengyue Li and
Wanrong Cao On Spectral Petrov--Galerkin Method for
Solving Optimal Control Problem Governed
by Fractional Diffusion Equations with
Fractional Noise . . . . . . . . . . . . ??
Ming-Jun Lai and
Zhaiming Shen A Compressed Sensing Based Least Squares
Approach to Semi-supervised Local
Cluster Extraction . . . . . . . . . . . ??
Wietse M. Boon and
Alessio Fumagalli A Reduced Basis Method for Darcy Flow
Systems that Ensures Local Mass
Conservation by Using Exact Discrete
Complexes . . . . . . . . . . . . . . . ??
Casey Garner and
Shuzhong Zhang Linearly-Convergent FISTA Variant for
Composite Optimization with Duality . . ??
Haitao Leng Error Estimates of EDG--HDG Methods for
the Stokes Equations with Dirac Measures ??
Carmelo Scribano and
Giorgia Franchini and
Marco Prato and
Marko Bertogna DCT-Former: Efficient Self-Attention
with Discrete Cosine Transform . . . . . ??
Chuqi Zheng and
Jiayu Qiu and
Qin Li and
Xinghui Zhong Stochastic Galerkin Methods for
Time-Dependent Radiative Transfer
Equations with Uncertain Coefficients ??
Jinda Yang and
Haiming Song and
Xinxin Li and
Di Hou Block Mirror Stochastic Gradient Method
For Stochastic Optimization . . . . . . ??
Dongdong Hu and
Yayun Fu and
Wenjun Cai and
Yushun Wang Unconditional Convergence of
Conservative Spectral Galerkin Methods
for the Coupled Fractional Nonlinear
Klein--Gordon--Schrödinger Equations . . ??
Christoph Lenz and
Luiz Felipe Aguinsky and
Andreas Hössinger and
Josef Weinbub A Complementary Topographic Feature
Detection Algorithm Based on Surface
Curvature for Three-Dimensional
Level-Set Functions . . . . . . . . . . ??
Mehdi Dehghan and
Zeinab Gharibi and
Ricardo Ruiz-Baier Optimal Error Estimates of Coupled and
Divergence-Free Virtual Element Methods
for the
Poisson--Nernst--Planck/Navier--Stokes
Equations and Applications in
Electrochemical Systems . . . . . . . . ??
Chinedu Izuchukwu and
Simeon Reich and
Yekini Shehu and
Adeolu Taiwo Strong Convergence of
Forward-Reflected-Backward Splitting
Methods for Solving Monotone Inclusions
with Applications to Image Restoration
and Optimal Control . . . . . . . . . . ??
Francesco Romor and
Giovanni Stabile and
Gianluigi Rozza Non-linear Manifold Reduced-Order Models
with Convolutional Autoencoders and
Reduced Over-Collocation Method . . . . ??
Yangyang Tang and
Guang-an Zou and
Jian Li Unconditionally Energy-Stable Finite
Element Scheme for the Chemotaxis--Fluid
System . . . . . . . . . . . . . . . . . ??
M. A. Hamadi and
K. Jbilou and
A. Ratnani A Data-Driven Krylov Model Order
Reduction for Large-Scale Dynamical
Systems . . . . . . . . . . . . . . . . ??
Alexander Zlotnik and
Raimondas Ciegis On Construction and Properties of
Compact 4th Order Finite-Difference
Schemes for the Variable Coefficient
Wave Equation . . . . . . . . . . . . . ??
Yulei Liao and
Pingbing Ming and
Yun Xu Taylor--Hood Like Finite Elements for
Nearly Incompressible Strain Gradient
Elasticity Problems . . . . . . . . . . ??
Guang-an Zou and
Zhaohua Li and
Xiaofeng Yang Fully Discrete Discontinuous Galerkin
Numerical Scheme with Second-Order
Temporal Accuracy for the
Hydrodynamically Coupled Lipid Vesicle
Model . . . . . . . . . . . . . . . . . ??
Silvia Bertoluzza and
Giovanna Guidoboni and
Romain Hild and
Daniele Prada and
Christophe Prud'homme and
Riccardo Sacco and
Lorenzo Sala and
Marcela Szopos A HDG Method for Elliptic Problems with
Integral Boundary Condition: Theory and
Applications . . . . . . . . . . . . . . ??
Mohamed Abd El-Hady Kassem Second-Order Symmetric Duality for
Multiple Objectives Nonlinear
Programming Under Generalizations of
Cone-Preinvexity Functions . . . . . . . ??
Sabine Le Borne and
Willi Leinen Guidelines for RBF--FD Discretization:
Numerical Experiments on the Interplay
of a Multitude of Parameter Choices . . ??
Peipei Lu and
Andreas Rupp and
Guido Kanschat Two-level Schwarz Methods for
Hybridizable Discontinuous Galerkin
Methods . . . . . . . . . . . . . . . . ??
B. Kheirfam Corrector--Predictor Interior-Point
Method With New Search Direction for
Semidefinite Optimization . . . . . . . ??
Nail K. Yamaleev and
Johnathon Upperman High-Order Positivity-Preserving Entropy
Stable Schemes for the $3$-D
Compressible Navier--Stokes Equations ??
Patrick Cheridito and
Balint Gersey Computation of Conditional Expectations
with Guarantees . . . . . . . . . . . . ??
Kisun Lee and
Xindong Tang On the Polyhedral Homotopy Method for
Solving Generalized Nash Equilibrium
Problems of Polynomials . . . . . . . . ??
Huimin Ma and
Pengzhan Huang A Fully Discrete Decoupled Finite
Element Method for the Thermally Coupled
Incompressible Magnetohydrodynamic
Problem . . . . . . . . . . . . . . . . ??
Lei Huang and
Jiawang Nie and
Ya-Xiang Yuan Generalized Truncated Moment Problems
with Unbounded Sets . . . . . . . . . . ??
Hailong Qiu Error Analysis of Fully Discrete Scheme
for the
Cahn--Hilliard--Magneto--Hydrodynamics
Problem . . . . . . . . . . . . . . . . ??
Amareshwara Sainadh Chamarthi and
Natan Hoffmann and
Hiroaki Nishikawa and
Steven H. Frankel Implicit Gradients Based Conservative
Numerical Scheme for Compressible Flows ??
Tianbai Xiao and
Jonas Kusch and
Julian Koellermeier and
Martin Frank A Flux Reconstruction Stochastic
Galerkin Scheme for Hyperbolic
Conservation Laws . . . . . . . . . . . ??
Erica R. Johnson and
James A. Rossmanith and
Christine Vaughan Positivity-Preserving Lax--Wendroff
Discontinuous Galerkin Schemes for
Quadrature-Based Moment-Closure
Approximations of Kinetic Models . . . . ??
Ruishu Wang and
Zhuoran Wang and
Jiangguo Liu Penalty-Free Any-Order Weak Galerkin
FEMs for Linear Elasticity on
Quadrilateral Meshes . . . . . . . . . . ??
Serpil Yalcin Kuzu Random Forest Based Multiclass
Classification Approach for Highly
Skewed Particle Data . . . . . . . . . . ??
Yue Wang and
Jiequan Li Stiffened Gas Approximation and GRP
Resolution for Compressible Fluid Flows
of Real Materials . . . . . . . . . . . ??
Anna Ivagnes and
Nicola Demo and
Gianluigi Rozza Towards a Machine Learning Pipeline in
Reduced Order Modelling for Inverse
Problems: Neural Networks for Boundary
Parametrization, Dimensionality
Reduction and Solution Manifold
Approximation . . . . . . . . . . . . . ??
Ying Ma and
Teng Zhang Error Estimates of Finite Difference
Methods for the Biharmonic Nonlinear
Schrödinger Equation . . . . . . . . . . ??
Bohan Yang and
Hongxing Rui A Robust Discrete Scheme based on
Staggered Grids for Poroelastic--Elastic
Coupled Problems . . . . . . . . . . . . ??
Zheng Ma and
Chengming Huang Fractional Collocation Method for
Third-Kind Volterra Integral Equations
with Nonsmooth Solutions . . . . . . . . ??
Yinkun Wang Parallel Numerical Picard Iteration
Methods . . . . . . . . . . . . . . . . ??
Yuling Jiao and
Dingwei Li and
Min Liu and
Xiliang Lu and
Yuanyuan Yang Just Least Squares: Binary Compressive
Sampling with Low Generative Intrinsic
Dimension . . . . . . . . . . . . . . . ??
Shijie Huang and
Xufeng Xiao and
Xinlong Feng An Adaptive Time-Stepping Method for the
Binary Fluid-Surfactant Phase Field
Model on Evolving Surfaces . . . . . . . ??
Keyi Wu and
Thomas O'Leary-Roseberry and
Peng Chen and
Omar Ghattas Large-Scale Bayesian Optimal
Experimental Design with
Derivative-Informed Projected Neural
Network . . . . . . . . . . . . . . . . ??
Ruchi Guo and
Jiahua Jiang and
Yi Li Learn an Index Operator by CNN for
Solving Diffusive Optical Tomography: a
Deep Direct Sampling Method . . . . . . ??
Lin Li and
Li-Lian Wang and
Huiyuan Li An Efficient Spectral Trust-Region
Deflation Method for Multiple Solutions ??
Mengqi Hu and
Yifei Lou and
Bao Wang and
Ming Yan and
Xiu Yang and
Qiang Ye Accelerated Sparse Recovery via Gradient
Descent with Nonlinear Conjugate
Gradient Momentum . . . . . . . . . . . ??
Jun Huang and
Gang Wu Truncated and Sparse Power Methods with
Partially Updating for Large and Sparse
Higher-Order PageRank Problems . . . . . ??
Naxian Ni and
Suchuan Dong Numerical Computation of Partial
Differential Equations by Hidden-Layer
Concatenated Extreme Learning Machine ??
Vít Dolejsí and
Georg May An Anisotropic hp-mesh Adaptation
Method for Time-Dependent Problems Based
on Interpolation Error Control . . . . . ??
Qianqian Liu and
Jianyu Jing and
Maoqin Yuan and
Wenbin Chen A Positivity-Preserving, Energy Stable
BDF2 Scheme with Variable Steps for the
Cahn--Hilliard Equation with Logarithmic
Potential . . . . . . . . . . . . . . . ??
Yifen Ke and
Changfeng Ma and
Zhigang Jia and
Yajun Xie and
Riwei Liao Quasi Non-Negative Quaternion Matrix
Factorization with Application to Color
Face Recognition . . . . . . . . . . . . ??
Qinsi Wang and
Wei Hong Yang Proximal Quasi-Newton Method for
Composite Optimization over the Stiefel
Manifold . . . . . . . . . . . . . . . . ??
Zheng Sun and
Yulong Xing On Generalized Gauss--Radau Projections
and Optimal Error Estimates of
Upwind-Biased DG Methods for the Linear
Advection Equation on Special Simplex
Meshes . . . . . . . . . . . . . . . . . ??
Rubén Aylwin and
Fernando Henríquez and
Christoph Schwab ReLU Neural Network Galerkin BEM . . . . ??
Chein-Shan Liu and
Lin Qiu Solving Nonlinear Elliptic Inverse
Source, Coefficient and Conductivity
Problems by the Methods with Bases
Satisfying the Boundary Conditions
Automatically . . . . . . . . . . . . . ??
Birgul Koc and
Tomás Chacón Rebollo and
Samuele Rubino Uniform Bounds with Difference Quotients
for Proper Orthogonal Decomposition
Reduced Order Models of the Burgers
Equation . . . . . . . . . . . . . . . . ??
I. S. Popov Space-Time Adaptive ADER--DG Finite
Element Method with LST--DG Predictor
and \em a posteriori Sub-cell WENO
Finite-Volume Limiting for Simulation of
Non-stationary Compressible
Multicomponent Reactive Flows . . . . . ??
W. A. Mulder Unisolvence of Symmetric Node Patterns
for Polynomial Spaces on the Simplex . . ??
Sining Gong and
Johnny Guzmán and
Michael Neilan A Note on the Shape Regularity of
Worsey--Farin Splits . . . . . . . . . . ??
Vinicius L. S. Silva and
Claire E. Heaney and
Yaqi Li and
Christopher C. Pain Correction to: Data Assimilation
Predictive GAN (DA-PredGAN) Applied to a
Spatio-Temporal Compartmental Model in
Epidemiology . . . . . . . . . . . . . . ??
Jiahui Zhang and
Yinhua Xia and
Yan Xu Moving Water Equilibria Preserving
Discontinuous Galerkin Method for the
Shallow Water Equations . . . . . . . . ??
Chuan Li and
Yiming Ren and
Guangqing Long and
Eric Boerman and
Shan Zhao A Fast Sine Transform Accelerated
High-Order Finite Difference Method for
Parabolic Problems over Irregular
Domains . . . . . . . . . . . . . . . . ??
Changxin Qiu and
Aaron Bendickson and
Joshua Kalyanapu and
Jue Yan Accuracy and Architecture Studies of
Residual Neural Network Method for
Ordinary Differential Equations . . . . ??
Dan Ling and
Zhiping Mao Analysis and Hermite Spectral
Approximation of Diffusive--Viscous Wave
Equations in Unbounded Domains Arising
in Geophysics . . . . . . . . . . . . . ??
Wandi Dong and
Gaohang Yu and
Liqun Qi and
Xiaohao Cai Practical Sketching Algorithms for
Low-Rank Tucker Approximation of Large
Tensors . . . . . . . . . . . . . . . . ??
Wasilij Barsukow All-Speed Numerical Methods for the
Euler Equations via a Sequential
Explicit Time Integration . . . . . . . ??
Justin Baker and
Elena Cherkaev and
Akil Narayan and
Bao Wang Learning Proper Orthogonal Decomposition
of Complex Dynamics Using Heavy-ball
Neural ODEs . . . . . . . . . . . . . . ??
Simon-Christian Klein Stabilizing Discontinuous Galerkin
Methods Using Dafermos' Entropy Rate
Criterion: I --- One-Dimensional
Conservation Laws . . . . . . . . . . . ??
Ming-Jun Lai and
Jinsil Lee Trivariate Spline Collocation Methods
for Numerical Solution to $3$D
Monge--Amp\`ere Equation . . . . . . . . ??
Yiqun Li and
Hong Wang and
Xiangcheng Zheng A viscoelastic Timoshenko Beam Model:
Regularity and Numerical Approximation ??
Chaoyu Quan and
Xu Wu Global-in-Time $ H^1 $-Stability of
L2-1$_\sigma $ Method on General
Nonuniform Meshes for Subdiffusion
Equation . . . . . . . . . . . . . . . . ??
Yunyun Ma and
Jiguang Sun Analysis of a Fourier--Galerkin Method
for the Transmission Eigenvalue Problem
based on a Boundary Integral Formulation ??
Ying He and
Xiaofei Zhao Numerical Methods for Some Nonlinear
Schrödinger Equations in Soliton
Management . . . . . . . . . . . . . . . ??
Lixiu Wang and
Qian Zhang and
Zhimin Zhang Superconvergence Analysis of
Curlcurl-Conforming Elements on
Rectangular Meshes . . . . . . . . . . . ??
Seokjun Ham and
Soobin Kwak and
Chaeyoung Lee and
Gyeonggyu Lee and
Junseok Kim A Second-order Time-Accurate
Unconditionally Stable Method for a
Gradient Flow for the Modica--Mortola
Functional . . . . . . . . . . . . . . . ??
Haotao Cai An Efficient Spectral-Galerkin Method
for Second Kind Weakly Singular VIEs
with Highly Oscillatory Kernels . . . . ??
André L. Marchildon and
David W. Zingg A Non-intrusive Solution to the
Ill-Conditioning Problem of the
Gradient-Enhanced Gaussian Covariance
Matrix for Gaussian Processes . . . . . ??
Bin Wang and
Yaolin Jiang Structure-Preserving Algorithms with
Uniform Error Bound and Long-time Energy
Conservation for Highly Oscillatory
Hamiltonian Systems . . . . . . . . . . ??
Jiangyong Hou and
Dan Hu and
Xuejian Li and
Xiaoming He Modeling and a Domain Decomposition
Method with Finite Element
Discretization for Coupled Dual-Porosity
Flow and Navier--Stokes Flow . . . . . . ??
S. Dirckx and
D. Huybrechs and
R. Ongenae On the Computation of the SVD of Fourier
Submatrices . . . . . . . . . . . . . . ??
Yang Xu and
Zhenguo Zhou and
Jingjun Zhao Error Estimates of Conforming Virtual
Element Methods with a Modified
Symmetric Nitsche's Formula for 2D
Semilinear Parabolic Equations . . . . . ??
Yifan Lin and
Zhen Gao and
Yuanhong Chen and
Xiang Sun A Dynamic Mode Decomposition Based
Reduced-Order Model For Parameterized
Time-Dependent Partial Differential
Equations . . . . . . . . . . . . . . . ??
Yao-Yuan Cai and
Hai-Wei Sun and
Sik-Chung Tam Numerical Study of a Fast Two-Level
Strang Splitting Method for Spatial
Fractional Allen--Cahn Equations . . . . ??
Yuchen Huang and
Weifeng Qiu and
Weiwei Sun New Analysis of Mixed Finite Element
Methods for Incompressible
Magnetohydrodynamics . . . . . . . . . . ??
Yuan Li and
Rong An Error Analysis of a Unconditionally
Stable BDF2 Finite Element Scheme for
the Incompressible Flows with Variable
Density . . . . . . . . . . . . . . . . ??
Hang Li and
Chunmei Su A Semi-discrete First-Order Low
Regularity Exponential Integrator for
the ``good'' Boussinesq Equation Without
Loss of Regularity . . . . . . . . . . . ??
Philippe G. LeFloch and
Jean-Marc Mercier A Class of Mesh-Free Algorithms for Some
Problems Arising in Finance and Machine
Learning . . . . . . . . . . . . . . . . ??
Zhe Ji and
Tian Liang and
Lin Fu High-Order Finite-Volume TENO Schemes
with Dual ENO-Like Stencil Selection for
Unstructured Meshes . . . . . . . . . . ??
Hans De Sterck and
Chi-Wang Shu and
Rémi Abgrall Enhancing Reproducibility of Research
Papers in SISC, JSC and JCP . . . . . . ??
Andrea Hanke and
Manuel Torrilhon Representation Theory Based Algorithm to
Compute Boltzmann's Bilinear Collision
Operator in the Irreducible Spectral
Burnett Ansatz Efficiently . . . . . . . ??
Gabriel N. Gatica and
Nicolás Núñez and
Ricardo Ruiz-Baier Mixed-Primal Methods for Natural
Convection Driven Phase Change with
Navier--Stokes--Brinkman Equations . . . ??
Qian Huang and
Yihong Chen and
Wen-An Yong Discrete-Velocity-Direction Models of
BGK-type with Minimum Entropy: I. Basic
Idea . . . . . . . . . . . . . . . . . . ??
Lina Zhao A Priori and a Posteriori Error Analysis
of TDNNS Method for Linear Elasticity
Problem Under Minimal Regularity . . . . ??
Daniel Drzisga and
Tobias Köppl and
Barbara Wohlmuth A Semi Matrix-Free Twogrid
Preconditioner for the Helmholtz
Equation with Near Optimal Shifts . . . ??
Kisun Lee and
Xindong Tang Correction to: On the Polyhedral
Homotopy Method for Solving Generalized
Nash Equilibrium Problems of Polynomials ??
Sergio Amat and
Zhilin Li and
Juan Ruiz-Álvarez and
Concepción Solano and
Juan C. Trillo Adapting Cubic Hermite Splines to the
Presence of Singularities Through
Correction Terms . . . . . . . . . . . . ??
Zheng Yang and
Fanhai Zeng A Corrected L1 Method for a
Time-Fractional Subdiffusion Equation ??
Hans De Sterck and
Chi-Wang Shu and
Rémi Abgrall Correction to: Enhancing Reproducibility
of Research Papers in SISC, JSC and JCP ??
Fei Wang and
Sheheryar Shah and
Bangmin Wu Discontinuous Galerkin Methods for
Hemivariational Inequalities in Contact
Mechanics . . . . . . . . . . . . . . . ??
Shuxun Shi and
Wenbin Chen Convergence and Asymptotic Stability of
the BDF Schemes for the Nonlocal Partial
Differential Equations with Delay . . . ??
Zhongqing Wang and
Xian Wen and
Guoqing Yao An Efficient Spectral-Galerkin Method
for Elliptic Equations in 2D Complex
Geometries . . . . . . . . . . . . . . . ??
Jie Du and
Yong Liu and
Yang Yang An Oscillation-Free Bound-Preserving
Discontinuous Galerkin Method for
Multi-component Chemically Reacting
Flows . . . . . . . . . . . . . . . . . ??
J. Gopalakrishnan and
L. Kogler and
P. L. Lederer and
J. Schöberl Divergence-Conforming Velocity and
Vorticity Approximations for
Incompressible Fluids Obtained with
Minimal Facet Coupling . . . . . . . . . ??
Gustav Eriksson Non-conforming Interface Conditions for
the Second-Order Wave Equation . . . . . ??
Seshadri R. Basava and
Winnifried Wollner Gradient Robust Mixed Methods for Nearly
Incompressible Elasticity . . . . . . . ??
Min Tao and
Xiao-Ping Zhang Study on $ L_1 $ over $ L_2 $
Minimization for Nonnegative Signal
Recovery . . . . . . . . . . . . . . . . ??
Xi Chen and
Alexander Kurganov and
Yongle Liu Flux Globalization Based Well-Balanced
Central-Upwind Schemes for Hydrodynamic
Equations with General Free Energy . . . ??
Jared Weed and
Lingyun Ding and
Jingfang Huang and
Min Hyung Cho Quadrature by Two Expansions for
Evaluating Helmholtz Layer Potentials ??
H. De Sterck and
R. D. Falgout and
O. A. Krzysik and
J. B. Schroder Efficient Multigrid Reduction-in-Time
for Method-of-Lines Discretizations of
Linear Advection . . . . . . . . . . . . ??
Xiaonian Long and
Qianqian Ding Convergence Analysis of the Fully
Discrete Projection Method for
Inductionless Magnetohydrodynamics
System Based on Charge Conservation . . ??
Dong-Ling Cai and
Jingyan Hu and
Yi-Bin Xiao and
Ping Zeng and
Guanyu Zhou A Fully-Discrete Finite Element Scheme
and Projection--Iteration Algorithm for
a Dynamic Contact Problem with
Multi-contact Zones and Unilateral
Constraint . . . . . . . . . . . . . . . ??
Yao Xiao and
Jan Glaubitz Sequential Image Recovery Using Joint
Hierarchical Bayesian Learning . . . . . ??
Wenqing Ouyang and
Jiong Tao and
Andre Milzarek and
Bailin Deng Nonmonotone Globalization for Anderson
Acceleration via Adaptive Regularization ??
Lifang Pei and
Yifei Li A Structure-Preserving Parametric Finite
Element Method for Area-Conserved
Generalized Curvature Flow . . . . . . . ??
Harsha Hutridurga and
Krishan Kumar and
Amiya K. Pani Discontinuous Galerkin Methods with
Generalized Numerical Fluxes for the
Vlasov--Viscous Burgers' System . . . . ??
Lan Wang and
Linghua Kong and
Meng Chen and
Pengfei Zhu and
Huacheng Guo Structure-Preserving Combined High-Order
Compact Schemes for Multiple Order
Spatial Derivatives Differential
Equations . . . . . . . . . . . . . . . ??
Subhajit Giri and
Shuvam Sen Phase Error Analysis of Implicit
Runge--Kutta Methods: New Classes of
Minimal Dissipation Low Dispersion High
Order Schemes . . . . . . . . . . . . . ??
Jing Sun and
Daxin Nie and
Weihua Deng An Efficient Numerical Algorithm for the
Model Describing the Competition Between
Super- and Sub-diffusions Driven by
Fractional Brownian Sheet Noise . . . . ??
Boscarino Sebastiano High-Order Semi-implicit Schemes for
Evolutionary Partial Differential
Equations with Higher Order Derivatives ??
Will Trojak and
Rob Watson and
Peter Vincent An Extended Range of Stable Flux
Reconstruction Schemes on Quadrilaterals
for Various Polynomial Bases . . . . . . ??
Wei Fan and
Xindi Hu and
Shengfeng Zhu Numerical Reconstruction of a
Discontinuous Diffusive Coefficient in
Variable-Order Time-Fractional
Subdiffusion . . . . . . . . . . . . . . ??
Bilel Bensaid and
Gaël Poëtte and
Rodolphe Turpault Deterministic Neural Networks
Optimization from a Continuous and
Energy Point of View . . . . . . . . . . ??
Yuxiang Liang and
Shun Zhang Least-Squares Methods with Nonconforming
Finite Elements for General Second-Order
Elliptic Equations . . . . . . . . . . . ??
Zhengfang Zhang and
Xiangjing Gao and
Xiaoliang Cheng Numerical Estimation of the Inverse
Eigenvalue Problem for a Weighted
Helmholtz Equation . . . . . . . . . . . ??
Manuel Calvo and
Lin Fu and
Juan I. Montijano and
Luis Rández Singly TASE Operators for the Numerical
Solution of Stiff Differential Equations
by Explicit Runge--Kutta Schemes . . . . ??
María Gabriela Armentano and
Ariel L. Lombardi and
Cecilia Penessi Robust Estimates in Balanced Norms for
Singularly Perturbed Reaction Diffusion
Equations Using Graded Meshes . . . . . ??
Shaotao Hu and
Yuanheng Wang and
Qiao-Li Dong Convergence Analysis of a New Bregman
Extragradient Method for Solving Fixed
Point Problems and Variational
Inequality Problems in Reflexive Banach
Spaces . . . . . . . . . . . . . . . . . ??
Rohit Khandelwal and
Kamana Porwal and
Tanvi Wadhawan Adaptive Quadratic Finite Element Method
for the Unilateral Contact Problem . . . ??
Haimei Wang and
Feng Wang and
Jinru Chen and
Haifeng Ji A Conforming Virtual Element Method
Based on Unfitted Meshes for the
Elliptic Interface Problem . . . . . . . ??
Shixi Wang and
Hai Bi and
Yidu Yang The Mixed Discontinuous Galerkin Method
for Transmission Eigenvalues for
Anisotropic Medium . . . . . . . . . . . ??
Phuoc-Toan Huynh and
Yanzhao Cao and
Thi-Thao-Phuong Hoang Fast and Accuracy-Preserving Domain
Decomposition Methods for Reduced
Fracture Models with Nonconforming Time
Grids . . . . . . . . . . . . . . . . . ??
Stephan Hilb and
Andreas Langer and
Martin Alkämper A Primal--Dual Finite Element Method for
Scalar and Vectorial Total Variation
Minimization . . . . . . . . . . . . . . ??
Alessandro Alla and
Hugo Oliveira and
Gabriele Santin HJB-RBF Based Approach for the Control
of PDEs . . . . . . . . . . . . . . . . ??
Arijit Hazra and
Dinshaw S. Balsara and
Praveen Chandrashekar and
Sudip K. Garain Multidimensional Generalized Riemann
Problem Solver for Maxwell's Equations ??
Haixia Dong and
Zhongshu Zhao and
Shuwang Li and
Wenjun Ying and
Jiwei Zhang Second Order Convergence of a Modified
MAC Scheme for Stokes Interface Problems ??
Wei Bian and
Fan Wu Accelerated Smoothing Hard Thresholding
Algorithms for $ \ell_0 $ Regularized
Nonsmooth Convex Regression Problem . . ??
Leo G. Rebholz and
Mengying Xiao The Effect of Anderson Acceleration on
Superlinear and Sublinear Convergence ??
Kai Yang High Order Conservative Schemes for the
Generalized Benjamin--Ono Equation on
the Unbounded Domain . . . . . . . . . . ??
Lalit Kumar and
Sivaji Ganesh Sista and
Konijeti Sreenadh A Linearized L1-Galerkin FEM for
Non-smooth Solutions of Kirchhoff Type
Quasilinear Time-Fractional
Integro--Differential Equation . . . . . ??
Haijin Wang and
Xiaobin Shi and
Qiang Zhang Stability and Error Estimates of Local
Discontinuous Galerkin Methods with
Implicit--Explicit Backward Difference
Formulas up to Fifth Order for
Convection--Diffusion Equation . . . . . ??
Jing An and
Ting Tan and
Zhimin Zhang A Novel Spectral Approximation and Error
Estimation for Transmission Eigenvalues
in Spherical Domains . . . . . . . . . . ??
Guoyu Zhang and
Chengming Huang and
Anatoly A. Alikhanov and
Baoli Yin A High-Order Discrete Energy Decay and
Maximum-Principle Preserving Scheme for
Time Fractional Allen--Cahn Equation . . ??
Xiangyu Bai and
Jiebao Sun and
Jie Shen and
Wenjuan Yao and
Zhichang Guo A Ginzburg--Landau-$ H^{-1} $ Model and
Its SAV Algorithm for Image Inpainting ??
Hongyi Li and
Zhen Peng and
Chengwei Pan and
Di Zhao Fast Gradient Method for Low-Rank Matrix
Estimation . . . . . . . . . . . . . . . ??
Cédric Boulbe and
Blaise Faugeras and
Guillaume Gros and
Francesca Rapetti Tokamak Free-Boundary Plasma Equilibrium
Computations in Presence of Non-Linear
Materials . . . . . . . . . . . . . . . ??
Xiaolin Li Element-Free Galerkin Analysis of Stokes
Problems Using the Reproducing Kernel
Gradient Smoothing Integration . . . . . ??
Mustafa Engin Danis and
Jue Yan A Generalized Framework for Direct
Discontinuous Galerkin Methods for
Nonlinear Diffusion Equations . . . . . ??
Chengjing Wang and
Peipei Tang A Dual Semismooth Newton Based Augmented
Lagrangian Method for Large-Scale
Linearly Constrained Sparse Group
Square-Root Lasso Problems . . . . . . . ??
Anita Gjesteland and
Magnus Svärd Convergence of Chandrashekar's
Second-Derivative Finite-Volume
Approximation . . . . . . . . . . . . . ??
Yijie Yang and
Yutong Li and
Chunlin Wu and
Yuping Duan A Convergent Iterative Support Shrinking
Algorithm for Non-Lipschitz Multi-phase
Image Labeling Model . . . . . . . . . . ??
Giorgia Franchini and
Federica Porta and
Valeria Ruggiero and
Ilaria Trombini Correction to: A Line Search Based
Proximal Stochastic Gradient Algorithm
with Dynamical Variance Reduction . . . ??
Fan Yu and
Minghua Chen Second-Order Error Analysis for Fractal
Mobile/Immobile Allen--Cahn Equation on
Graded Meshes . . . . . . . . . . . . . ??
Hao Chen and
Alfio Borz\`\i Positivity Preserving Exponential
Integrators for Differential Riccati
Equations . . . . . . . . . . . . . . . ??
H. T. Huynh Discontinuous Galerkin and Related
Methods for ODE . . . . . . . . . . . . ??
Aziz Takhirov and
Aytekin Çìbìk and
Fatma G. Eroglu and
Songül Kaya An Improved Arrow--Hurwicz Method for
the Steady--State Navier--Stokes
Equations . . . . . . . . . . . . . . . ??
Mirco Ciallella and
Davide Torlo and
Mario Ricchiuto Arbitrary High Order WENO Finite Volume
Scheme with Flux Globalization for
Moving Equilibria Preservation . . . . . ??
Hongfei Fu and
Bingyin Zhang and
Xiangcheng Zheng A High-Order Two-Grid Difference Method
for Nonlinear Time-Fractional Biharmonic
Problems and Its Unconditional $ \alpha
$-Robust Error Estimates . . . . . . . . ??
Eric Chung and
Wing Tat Leung and
Sai-Mang Pun and
Zecheng Zhang Multi-agent Reinforcement Learning Aided
Sampling Algorithms for a Class of
Multiscale Inverse Problems . . . . . . ??
Alexander Kurganov and
Ruixiao Xin New Low-Dissipation Central-Upwind
Schemes . . . . . . . . . . . . . . . . ??
Xiuxiu Xu and
Qiumei Huang Discontinuous Galerkin Time Stepping for
Semilinear Parabolic Problems with Time
Constant Delay . . . . . . . . . . . . . ??
Yuling Jiao and
Dingwei Li and
Min Liu and
Xiliang Lu and
Yuanyuan Yang Correction to: Just Least Squares:
Binary Compressive Sampling with Low
Generative Intrinsic Dimension . . . . . ??
Xiu Yang and
Li-Lian Wang and
Huiyuan Li and
Changtao Sheng Müntz Ball Polynomials and Müntz
Spectral-Galerkin Methods for Singular
Eigenvalue Problems . . . . . . . . . . ??
Clemens Pechstein A Unified Theory of Non-overlapping
Robin--Schwarz Methods: Continuous and
Discrete, Including Cross Points . . . . ??
Xiubo Liang and
Guoqiang Wang and
Bo Yu A Reduced Half Thresholding Algorithm ??
Tianyang Chu and
Jilu Wang and
Na Wang and
Zhimin Zhang Optimal-Order Convergence of a Two--Step
BDF Method for the Navier--Stokes
Equations with $ H^1 $ Initial Data . . ??
Roberto Garrappa and
Andrea Giusti A Computational Approach to
Exponential-Type Variable-Order
Fractional Differential Equations . . . ??
Benjamin M. Kent and
Catherine E. Powell and
David J. Silvester and
Ma\lgorzata J. Zimo\'n Efficient Adaptive Stochastic
Collocation Strategies for
Advection--Diffusion Problems with
Uncertain Inputs . . . . . . . . . . . . ??
Giuseppe Patané Spectral Laplace Transform of Signals on
Arbitrary Domains . . . . . . . . . . . ??
Jian Meng Discontinuous Galerkin Method for the
Interior Transmission Eigenvalue Problem
in Inverse Scattering Theory . . . . . . ??
Shimin Zhao and
Tao Yan and
Kai Wang and
Yuanguo Zhu Adaptive Trust-Region Method on
Riemannian Manifold . . . . . . . . . . ??
Jun Li and
Yaolin Jiang Analysis of a New Accelerated Waveform
Relaxation Method Based on the
Time-Parallel Algorithm . . . . . . . . ??
Xu Li and
Hongxing Rui A Modified Convective Formulation in
Navier--Stokes Simulations . . . . . . . ??
Lu Cheng and
Kuan Xu Solving Time-Dependent PDEs with the
Ultraspherical Spectral Method . . . . . ??
Ruiyi Xie and
Boying Wu and
Wenjie Liu Optimal Error Estimates for Chebyshev
Approximations of Functions with
Endpoint Singularities in Fractional
Spaces . . . . . . . . . . . . . . . . . ??
Siyun Zhou and
Xin Liu and
Liwei Xu Stochastic Gauss--Newton Algorithms for
Online PCA . . . . . . . . . . . . . . . ??
Hongmin Su and
Jinsheng Cai and
Shucheng Pan and
Xiangyu Hu Reformulated Dissipation for the
Free-Stream Preserving of the
Conservative Finite Difference Schemes
on Curvilinear Grids . . . . . . . . . . ??
Yongchao Zhang and
Liquan Mei and
Gang Wang A Posteriori Error Analysis of the
Hybrid High-Order Method for the Stokes
Problem . . . . . . . . . . . . . . . . ??
Wenbin Chen and
Jianyu Jing and
Hao Wu A Uniquely Solvable,
Positivity-Preserving and
Unconditionally Energy Stable Numerical
Scheme for the Functionalized
Cahn--Hilliard Equation with Logarithmic
Potential . . . . . . . . . . . . . . . ??
Deliang Wei and
Fang Li and
Shiyang Weng Cauchy Noise Removal via Convergent
Plug-and-Play Framework with Outliers
Detection . . . . . . . . . . . . . . . ??
Zhuohang Wu and
Yu-xin Ren The Compact and Accuracy Preserving
Limiter for High-Order Finite Volume
Schemes Solving Compressible Flows . . . ??
Yuyu He and
Hongtao Chen Decoupled and Unconditionally Energy
Stable Finite Element Schemes for
Electrohydrodynamic Model with Variable
Density . . . . . . . . . . . . . . . . ??
Bengt Fornberg and
Cécile Piret Computation of Fractional Derivatives of
Analytic Functions . . . . . . . . . . . ??
Yao Xiao and
Anne Gelb and
Guohui Song Sequential Edge Detection Using Joint
Hierarchical Bayesian Learning . . . . . ??
Luka Grubisi\'c and
Ralf Hiptmair and
Diego Renner Detecting Near Resonances in Acoustic
Scattering . . . . . . . . . . . . . . . ??
Wenqiang Xiao and
Min Ling Virtual Element Method for a
History-Dependent
Variational-Hemivariational Inequality
in Contact Problems . . . . . . . . . . ??
Muyassar Ahmat and
Jianxian Qiu Hybrid HWENO Method for Nonlinear
Degenerate Parabolic Equations . . . . . ??
Fan Zhang and
Jian Cheng and
Tiegang Liu A Physical-Constraint-Preserving
Discontinuous Galerkin Method for Weakly
Compressible Two-Phase Flows . . . . . . ??
Qihao Ye and
Xiaochuan Tian Monotone Meshfree Methods for Linear
Elliptic Equations in Non-divergence
Form via Nonlocal Relaxation . . . . . . ??
Dan Gordon Conjugate Gradients Acceleration of
Coordinate Descent for Linear Systems ??
Rodolfo Araya and
Franz Chouly Residual a Posteriori Error Estimation
for Frictional Contact with Nitsche
Method . . . . . . . . . . . . . . . . . ??
C. Escalante and
E. D. Fernández-Nieto and
J. Garres-D\'ìaz and
A. Mangeney Multilayer Shallow Model for Dry
Granular Flows with a Weakly
Non-hydrostatic Pressure . . . . . . . . ??
Abhinav Singh and
Alejandra Foggia and
Pietro Incardona and
Ivo F. Sbalzarini A Meshfree Collocation Scheme for
Surface Differential Operators on Point
Clouds . . . . . . . . . . . . . . . . . ??
Waixiang Cao Unified Analysis of Any Order Spectral
Volume Methods for Diffusion Equations ??
Zhechen Zhang and
Sanyang Liu and
Zhiping Lin A Generalized Non-convex Method for
Robust Tensor Completion . . . . . . . . ??
Zhong-bao Wang and
Zhen-yin Lei and
Xin Long and
Zhang-you Chen A Modified Tseng Splitting Method with
Double Inertial Steps for Solving
Monotone Inclusion Problems . . . . . . ??
Zhong-Feng Sun and
Jin-Chuan Zhou and
Yun-Bin Zhao Heavy-Ball-Based Optimal Thresholding
Algorithms for Sparse Linear Inverse
Problems . . . . . . . . . . . . . . . . ??
Xiaojing Xu and
Song Jiang and
Wenjun Sun Spatial Second-Order Positive and
Asymptotic Preserving Unified Gas
Kinetic Schemes for Radiative Transfer
Equations . . . . . . . . . . . . . . . ??
Wei Chen and
Jun Hu and
Min Zhang Nonconforming Finite Element Methods of
Order Two and Order Three for the Stokes
Flow in Three Dimensions . . . . . . . . ??
Nicola Guglielmi and
Anton Savostianov and
Francesco Tudisco Quantifying the Structural Stability of
Simplicial Homology . . . . . . . . . . ??
Yunlong Wang and
Chungen Shen and
Lei-Hong Zhang and
Wei Hong Yang Proximal Gradient/Semismooth Newton
Methods for Projection onto a Polyhedron
via the Duality-Gap--Active-Set Strategy ??
Abhijit Biswas and
David I. Ketcheson Multiple-Relaxation Runge Kutta Methods
for Conservative Dynamical Systems . . . ??
Wenyu Lei and
George Turkiyyah and
Omar Knio Finite Element Discretizations for
Variable-Order Fractional Diffusion
Problems . . . . . . . . . . . . . . . . ??
Jun Hu and
Hao Luo and
Zihang Zhang A Fast Solver for Generalized Optimal
Transport Problems Based on Dynamical
System and Algebraic Multigrid . . . . . ??
Jingwei Li and
Rihui Lan and
Yongyong Cai and
Lili Ju and
Xiaoqiang Wang Second-Order Semi--Lagrangian
Exponential Time Differencing Method
with Enhanced Error Estimate for the
Convective Allen--Cahn Equation . . . . ??
Chieh-Sen Huang and
Todd Arbogast and
Chenyu Tian Multidimensional WENO--AO
Reconstructions Using a Simplified
Smoothness Indicator and Applications to
Conservation Laws . . . . . . . . . . . ??
Andrea Thomann and
Michael Dumbser Thermodynamically Compatible
Discretization of a Compressible
Two-Fluid Model with Two Entropy
Inequalities . . . . . . . . . . . . . . ??
P. Díaz and
E. Mainar and
B. Rubio Polynomial Total Positivity and High
Relative Accuracy Through Schur
Polynomials . . . . . . . . . . . . . . ??
Gianluca Frasca-Caccia and
Pranav Singh Optimal Parameters for Numerical Solvers
of PDEs . . . . . . . . . . . . . . . . ??
Song Lu and
Xianmin Xu Numerical Investigations on Trace Finite
Element Methods for the
Laplace--Beltrami Eigenvalue Problem . . ??
Dorian Hillebrand and
Simon-Christian Klein and
Philipp Öffner Applications of Limiters, Neural
Networks and Polynomial Annihilation in
Higher-Order FD\slash FV Schemes . . . . ??
Harald Garcke and
Robert Nürnberg and
Quan Zhao Unfitted Finite Element Methods for
Axisymmetric Two-Phase Flow . . . . . . ??
Dakang Cen and
Caixia Ou and
Seakweng Vong Corrected $L$-type Method for
Multi-singularity Problems Arising from
Delay Fractional Equations . . . . . . . ??
Yingzhi Xia and
Qifeng Liao and
Jinglai Li VI-DGP: A Variational Inference Method
with Deep Generative Prior for Solving
High-Dimensional Inverse Problems . . . ??
Tian-Yi Li and
Fang Chen and
Hai-Wei Sun and
Tao Sun Preconditioning Technique Based on Sine
Transformation for Nonlocal Helmholtz
Equations with Fractional Laplacian . . ??
Daniel Acosta-Soba and
Francisco Guillén-González and
J. Rafael Rodríguez-Galván An Unconditionally Energy Stable and
Positive Upwind DG Scheme for the
Keller--Segel Model . . . . . . . . . . ??
Huadong Gao and
Wen Xie A Finite Element Method for the
Dynamical Ginzburg--Landau Equations
under Coulomb Gauge . . . . . . . . . . ??
Yiying Fang and
Ying Jiang A Fully Discrete High-Order Fast
Multiscale Galerkin Method for Solving
Boundary Integral Equations in a Domain
with Corners . . . . . . . . . . . . . . ??
Zhongxiao Jia and
Kailiang Zhang A FEAST SVDsolver Based on
Chebyshev--Jackson Series for Computing
Partial Singular Triplets of Large
Matrices . . . . . . . . . . . . . . . . ??
Gerard Awanou The Second Boundary Value Problem for a
Discrete Monge--Amp\`ere Equation . . . ??
Chun Liu and
Cheng Wang and
Steven M. Wise and
Xingye Yue and
Shenggao Zhou A Second Order Accurate, Positivity
Preserving Numerical Method for the
Poisson--Nernst--Planck System and Its
Convergence Analysis . . . . . . . . . . ??
Jingyan Hu and
Guanyu Zhou The Well-Posedness and Discontinuous
Galerkin Approximation for the
Non--Newtonian
Stokes--Darcy--Forchheimer Coupling
System . . . . . . . . . . . . . . . . . ??
Dhwanit Agarwal and
Michael O'Neil and
Manas Rachh FMM-Accelerated Solvers for the
Laplace--Beltrami Problem on Complex
Surfaces in Three Dimensions . . . . . . ??
Xinan Chen and
Anh Phong Tran and
Rena Elkin and
Helene Benveniste and
Allen R. Tannenbaum Visualizing Fluid Flows via Regularized
Optimal Mass Transport with Applications
to Neuroscience . . . . . . . . . . . . ??
Raman Kumar and
Bhupen Deka Optimal A Priori Error Estimates for
Elliptic Interface Problems: Weak
Galerkin Mixed Finite Element
Approximations . . . . . . . . . . . . . ??
M. Liu and
J. Dong and
Z. Li and
D. F. Li A Modified High-Resolution Non-staggered
Central Scheme with Adjustable Numerical
Dissipation . . . . . . . . . . . . . . ??
Lu Wang and
Hui Liang Superconvergence and Postprocessing of
Collocation Methods for Fractional
Differential Equations . . . . . . . . . ??
Xiao Bai and
Maojun Li A Conservative Sharp-Interface Numerical
Method for Two-dimensional Compressible
Two-phase Flows . . . . . . . . . . . . ??
Shiwei Liu and
Li Yuan A Modified A Posteriori Subcell Limiter
for High Order Flux Reconstruction
Scheme for One-Dimensional Detonation
Simulation . . . . . . . . . . . . . . . ??
Zhaoxiang Li and
Feng Zhang and
Jianxin Zhou Partial Newton-Correction Method for
Multiple Fixed Points of Semi-linear
Differential Operators by
Legendre--Gauss--Lobatto Pseudospectral
Method . . . . . . . . . . . . . . . . . ??
Abram Rodgers and
Daniele Venturi Implicit Integration of Nonlinear
Evolution Equations on Tensor Manifolds ??
Arnesh Sujanani and
Renato D. C. Monteiro An Adaptive Superfast Inexact Proximal
Augmented Lagrangian Method for Smooth
Nonconvex Composite Optimization
Problems . . . . . . . . . . . . . . . . ??
Nicola Rares Franco and
Andrea Manzoni and
Paolo Zunino Mesh-Informed Neural Networks for
Operator Learning in Finite Element
Spaces . . . . . . . . . . . . . . . . . ??
Derk Frerichs-Mihov and
Linus Henning and
Volker John Using Deep Neural Networks for Detecting
Spurious Oscillations in Discontinuous
Galerkin Solutions of
Convection-Dominated
Convection--Diffusion Equations . . . . ??
Cesare Bracco and
Francesco Calabr\`o and
Carlotta Giannelli Discontinuity Detection by Null Rules
for Adaptive Surface Reconstruction . . ??
Kai Diethelm and
Frank Uhlig A New Approach to Shooting Methods for
Terminal Value Problems of Fractional
Differential Equations . . . . . . . . . ??
Zhenyuan Zhu and
Fan Chen and
Junyu Zhang and
Zaiwen Wen A Unified Primal--Dual Algorithm
Framework for Inequality Constrained
Problems . . . . . . . . . . . . . . . . ??
Zhichao Peng and
Daniel Appelö and
Shuang Liu Universal AMG Accelerated Embedded
Boundary Method Without Small Cell
Stiffness . . . . . . . . . . . . . . . ??
Zhigang Jia and
Qianyu Wang and
Hong-Kui Pang and
Meixiang Zhao Computing Partial Quaternion Eigenpairs
with Quaternion Shift . . . . . . . . . ??
Xinfu Chen and
Zhengyang Lu and
Jingtang Ma and
Jinye Shen An Implicit Scheme for American Put
Options . . . . . . . . . . . . . . . . ??
Chaobao Huang and
Na An and
Hu Chen and
Xijun Yu $ \alpha $-Robust Error Analysis of Two
Nonuniform Schemes for Subdiffusion
Equations with Variable-Order
Derivatives . . . . . . . . . . . . . . ??
A. Buccini and
P. Díaz de Alba and
F. Pes and
L. Reichel An Efficient Implementation of the
Gauss--Newton Method Via Generalized
Krylov Subspaces . . . . . . . . . . . . ??
Fugui Ma and
Lijing Zhao and
Weihua Deng and
Yejuan Wang Analyses of the Contour Integral Method
for Time Fractional Normal-Subdiffusion
Transport Equation . . . . . . . . . . . ??
Qihao Ye and
Xiaochuan Tian Correction to: Monotone Meshfree Methods
for Linear Elliptic Equations in
Non-divergence Form via Nonlocal
Relaxation . . . . . . . . . . . . . . . ??
Josie König and
Melina A. Freitag Time-Limited Balanced Truncation for
Data Assimilation Problems . . . . . . . ??
Mingchao Cai and
Huipeng Gu and
Jingzhi Li and
Mo Mu Some Optimally Convergent Algorithms for
Decoupling the Computation of Biot's
Model . . . . . . . . . . . . . . . . . ??
Jonathan Popa and
Yifei Lou and
Susan E. Minkoff Low-Rank Tensor Data Reconstruction and
Denoising via ADMM: Algorithm and
Convergence Analysis . . . . . . . . . . ??
Pascal Mossier and
Daniel Appel and
Andrea D. Beck and
Claus-Dieter Munz An Efficient hp-Adaptive Strategy for a
Level-Set Ghost-Fluid Method . . . . . . ??
Yangshuai Wang and
Hao Wang Efficient a Posteriori Error Control of
a Concurrent Multiscale Method with
Sharp Interface for Crystalline Defects ??
Yaman Güçlü and
Said Hadjout and
Martin Campos Pinto A Broken FEEC Framework for
Electromagnetic Problems on Mapped
Multipatch Domains . . . . . . . . . . . ??
Yu Gao and
Hongyu Liu and
Xianchao Wang and
Kai Zhang A Bayesian Scheme for Reconstructing
Obstacles in Acoustic Waveguides . . . . ??
Danilo Amigo and
Felipe Lepe and
Gonzalo Rivera A Virtual Element Method for the
Elasticity Spectral Problem Allowing for
Small Edges . . . . . . . . . . . . . . ??
Fang Li and
Xiao-Guang Lv A Nonconvex Nonsmooth Image Prior Based
on the Hyperbolic Tangent Function . . . ??
Yongbin Han and
Yanren Hou Analysis of an Embedded-Hybridized
Discontinuous Galerkin Method for the
Time-Dependent Incompressible
Navier--Stokes Equations . . . . . . . . ??
Maxim Olshanskii and
Yerbol Palzhanov and
Annalisa Quaini A Scalar Auxiliary Variable Unfitted FEM
for the Surface Cahn--Hilliard Equation ??
Junqing Jia and
Xiaoyun Jiang Improved Uniform Error Bounds of
Exponential Wave Integrator Method for
Long-Time Dynamics of the Space
Fractional Klein--Gordon Equation with
Weak Nonlinearity . . . . . . . . . . . ??
Liet Vo Higher Order Time Discretization Method
for the Stochastic Stokes Equations with
Multiplicative Noise . . . . . . . . . . ??
Aycil Cesmelioglu and
Jeonghun J. Lee and
Sander Rhebergen Analysis of an Embedded-Hybridizable
Discontinuous Galerkin Method for Biot's
Consolidation Model . . . . . . . . . . ??
Sergio Carrasco and
Sergio Caucao and
Gabriel N. Gatica New Mixed Finite Element Methods for the
Coupled Convective Brinkman--Forchheimer
and Double-Diffusion Equations . . . . . ??
Yoshio Komori and
Kevin Burrage Split S-ROCK Methods for
High-Dimensional Stochastic Differential
Equations . . . . . . . . . . . . . . . ??
Yanwei Li and
Qiming Wang and
Zhaojie Zhou Adaptive Virtual Element Method for
Optimal Control Problem Governed by
Stokes Equations . . . . . . . . . . . . ??
Qiong-Ao Huang and
Wei Jiang and
Jerry Zhijian Yang and
Cheng Yuan A Structure-Preserving, Upwind-SAV
Scheme for the Degenerate Cahn--Hilliard
Equation with Applications to Simulating
Surface Diffusion . . . . . . . . . . . ??
Christophe Berthon and
Manuel J. Castro Díaz and
Arnaud Duran and
Tomás Morales de Luna and
Khaled Saleh Artificial Viscosity to Get Both
Robustness and Discrete Entropy
Inequalities . . . . . . . . . . . . . . ??
Qinian Jin On Convergence Rates of Proximal
Alternating Direction Method of
Multipliers . . . . . . . . . . . . . . ??
Zhenwei Zhang and
Huibin Chang and
Yuping Duan Fast Non-overlapping Domain
Decomposition Methods for Continuous
Multi-phase Labeling Problem . . . . . . ??
Li Zeng and
Xiaoliang Wan and
Tao Zhou Adaptive Deep Density Approximation for
Fractional Fokker--Planck Equations . . ??
Nawfel Benatia and
Abdellah El Kacimi and
Omar Laghrouche and
Ahmed Ratnani Bernstein--Bézier $ H({\rm curl})
$-Conforming Finite Elements for
Time-Harmonic Electromagnetic Scattering
Problems . . . . . . . . . . . . . . . . ??
Lukás Vacek and
Václav Kucera Godunov-Like Numerical Fluxes for
Conservation Laws on Networks . . . . . ??
Dongfang Li and
Xiaoxi Li and
Hai-wei Sun Optimal Error Estimates of SAV
Crank--Nicolson Finite Element Method
for the Coupled Nonlinear Schrödinger
Equation . . . . . . . . . . . . . . . . ??
Deepak Bhoriya and
Biswarup Biswas and
Harish Kumar and
Praveen Chandrashekhar Entropy Stable Discontinuous Galerkin
Schemes for Two-Fluid Relativistic
Plasma Flow Equations . . . . . . . . . ??
K. R. Arun and
Rahuldev Ghorai and
Mainak Kar An Asymptotic Preserving and Energy
Stable Scheme for the Barotropic Euler
System in the Incompressible Limit . . . ??
Yaman Güçlü and
Said Hadjout and
Martin Campos Pinto Correction: A Broken FEEC Framework for
Electromagnetic Problems on Mapped
Multipatch Domains . . . . . . . . . . . ??
Yayun Fu and
Xuelong Gu and
Yushun Wang and
Wenjun Cai Mass-, and Energy Preserving Schemes
with Arbitrarily High Order for the
Klein--Gordon--Schrödinger Equations . . ??
Ang Ge and
Jinye Shen and
Seakweng Vong Space-Time Methods Based on Isogeometric
Analysis for Time-fractional Schrödinger
Equation . . . . . . . . . . . . . . . . ??
Anshu Yadav and
Deepak Bhoriya and
Harish Kumar and
Praveen Chandrashekar Entropy Stable Schemes for the Shear
Shallow Water Model Equations . . . . . ??
Qichen Liao and
Zihao Wang and
Jing Chen and
Bo Bai and
Shi Jin and
Hao Wu Fast Sinkhorn II: Collinear Triangular
Matrix and Linear Time Accurate
Computation of Optimal Transport . . . . ??
Guiyun Xiao and
Shuqin Zhang and
Zheng-Jian Bai Scaled Proximal Gradient Methods for
Sparse Optimization Problems . . . . . . ??
Ping-Fan Dai and
Jianchao Bai and
Jicheng Li A General Preconditioner for Tensor
Complementarity Problems . . . . . . . . ??
Chen Liu and
Yuan Gao and
Xiangxiong Zhang Structure Preserving Schemes for
Fokker--Planck Equations of Irreversible
Processes . . . . . . . . . . . . . . . ??
Yang Jing and
Jiaheng Chen and
Lei Li and
Jianfeng Lu A Machine Learning Framework for
Geodesics Under Spherical
Wasserstein--Fisher--Rao Metric and Its
Application for Weighted Sample
Generation . . . . . . . . . . . . . . . ??
Gouranga Mallik and
Thirupathi Gudi A Hybrid High-Order Method for a Class
of Strongly Nonlinear Elliptic Boundary
Value Problems . . . . . . . . . . . . . ??
Liliana Camargo and
Bibiana López-Rodríguez and
Mauricio Osorio and
Manuel Solano An Adaptive and Quasi-periodic HDG
Method for Maxwell's Equations in
Heterogeneous Media . . . . . . . . . . ??
S. Langer and
R. C. Swanson Implementation, Realization and an
Effective Solver of Two-Equation
Turbulence Models . . . . . . . . . . . ??
Yunfei Qu and
Hongjin He and
Deren Han A Partially Inertial Customized
Douglas--Rachford Splitting Method for a
Class of Structured Optimization
Problems . . . . . . . . . . . . . . . . ??
Zhen Miao and
Bin Wang and
Yao-Lin Jiang Numerical Conservations of Energy,
Momentum and Actions in the Full
Discretisation for Nonlinear Wave
Equations . . . . . . . . . . . . . . . ??
Fei Xu and
Shuangshuang Chen and
Fusheng Luo A Novel Domain Decomposition Method for
Eigenvalue Problems . . . . . . . . . . ??
Jinping Yang and
Charles Wing Ho Green and
Amiya K. Pani and
Yubin Yan Unconditionally Stable and Convergent
Difference Scheme for Superdiffusion
with Extrapolation . . . . . . . . . . . ??
Ilya Chevyrev and
Andris Gerasimovics and
Hendrik Weber Feature Engineering with Regularity
Structures . . . . . . . . . . . . . . . ??
Kirill Serkh and
James Bremer Phase Function Methods for Second Order
Inhomogeneous Linear Ordinary
Differential Equations . . . . . . . . . ??
Travis Askham and
Carlos Borges and
Jeremy Hoskins and
Manas Rachh Random Walks in Frequency and the
Reconstruction of Obstacles with
Cavities from Multi-frequency Data . . . ??
Wen-Jie Zheng and
Xi-Le Zhao and
Yu-Bang Zheng and
Ting-Zhu Huang Provable Stochastic Algorithm for
Large-Scale Fully-Connected Tensor
Network Decomposition . . . . . . . . . ??
Xinyuan Zhang and
Xiang Wang The Hermite Finite Volume Method with
Global Conservation Law . . . . . . . . ??
Xiuling Hu and
Lulu Cheng Numerical Analysis of a Convex-Splitting
BDF2 Method with Variable Time-Steps for
the Cahn--Hilliard Model . . . . . . . . ??
Yuan Chen and
Xu Zhang Solving Navier--Stokes Equations with
Stationary and Moving Interfaces on
Unfitted Meshes . . . . . . . . . . . . ??
Afsaneh Moradi and
Ali Abdi and
Gholamreza Hojjati Strong Stability Preserving Second
Derivative General Linear Methods Based
on Taylor Series Conditions for
Discontinuous Galerkin Discretizations ??
Jai Tushar and
Ramesh Chandra Sau and
Anil Kumar Virtual Element Method for Control
Constrained Dirichlet Boundary Control
Problem Governed by the Diffusion
Problem . . . . . . . . . . . . . . . . ??
Li Liu and
Shengping Liu and
Hui Xie and
Fansheng Xiong and
Tengchao Yu and
Mengjuan Xiao and
Lufeng Liu and
Heng Yong Discontinuity Computing Using
Physics-Informed Neural Networks . . . . ??
Salman Ahmadi-Asl and
Anh-Huy Phan and
Andrzej Cichocki A Randomized Algorithm for Tensor
Singular Value Decomposition Using an
Arbitrary Number of Passes . . . . . . . ??
Guanjie Wang and
Smita Sahu and
Qifeng Liao An Adaptive ANOVA Stochastic Galerkin
Method for Partial Differential
Equations with High-dimensional Random
Inputs . . . . . . . . . . . . . . . . . ??
Eric Canc\`es and
Gaspard Kemlin and
Antoine Levitt A Priori Error Analysis of Linear and
Nonlinear Periodic Schrödinger Equations
with Analytic Potentials . . . . . . . . ??
Hanyu Chu and
Yongzhong Song and
Haifeng Ji and
Ying Cai Multigrid Algorithm for Immersed Finite
Element Discretizations of Elliptic
Interface Problems . . . . . . . . . . . ??
Lei Yang and
Yuan Liu and
Yan Jiang and
Mengping Zhang Discontinuous Galerkin Methods for
Network Patterning Phase-Field Models ??
Daniela Capatina and
Aimene Gouasmi and
Cuiyu He Robust Flux Reconstruction and a
Posteriori Error Analysis for an
Elliptic Problem with Discontinuous
Coefficients . . . . . . . . . . . . . . ??
Wei-Hung Liao and
Tsung-Ming Huang and
Wen-Wei Lin and
Mei-Heng Yueh Convergence of Dirichlet Energy
Minimization for Spherical Conformal
Parameterizations . . . . . . . . . . . ??
Jan Glaubitz and
Jan Nordström and
Philipp Öffner Energy-Stable Global Radial Basis
Function Methods on Summation-By-Parts
Form . . . . . . . . . . . . . . . . . . ??
Feifei Jing and
Weimin Han and
Takahito Kashiwabara and
Wenjing Yan On Finite Volume Methods for a
Navier--Stokes Variational Inequality ??
Fernando V. Ravelo and
Pedro S. Peixoto and
Martin Schreiber An Explicit Exponential Integrator Based
on Faber Polynomials and its Application
to Seismic Wave Modeling . . . . . . . . ??
Alexandra Baumgart and
Samuel W. Jones and
Philipp V. F. Edelmann and
Joshua C. Dolence A Shock Stabilization of the HLLC
Riemann Solver for the Carbuncle
Instability . . . . . . . . . . . . . . ??
Claudius Birke and
Walter Boscheri and
Christian Klingenberg A Well-Balanced Semi-implicit IMEX
Finite Volume Scheme for Ideal
Magnetohydrodynamics at All Mach Numbers ??
Yaoyao Chen and
Yunqing Huang and
Nianyu Yi and
Peimeng Yin Recovery Type a Posteriori Error
Estimation of an Adaptive Finite Element
Method for Cahn--Hilliard Equation . . . ??
Fan Jia and
Tiange Wang and
Tieyong Zeng Low-light Image Enhancement via Dual
Reflectance Estimation . . . . . . . . . ??
Ngoc Mai Monica Huynh Convergence Analysis for Virtual Element
Discretizations of the Cardiac Bidomain
Model . . . . . . . . . . . . . . . . . ??
Dibyendu Adak and
Gianmarco Manzini and
Hashem M. Mourad and
JeeYeon N. Plohr and
Lampros Svolos A $ C^1 $-Conforming Arbitrary-Order
Two-Dimensional Virtual Element Method
for the Fourth-Order Phase-Field
Equation . . . . . . . . . . . . . . . . ??
Endre Kovács and
János Majár and
Mahmoud Saleh Unconditionally Positive, Explicit,
Fourth Order Method for the Diffusion-
and Nagumo-Type Diffusion--Reaction
Equations . . . . . . . . . . . . . . . ??
Farid Bozorgnia and
Leon Bungert and
Daniel Tenbrinck The Infinity Laplacian Eigenvalue
Problem: Reformulation and a Numerical
Scheme . . . . . . . . . . . . . . . . . ??
Longfei Li and
Hangjie Ji and
Qi Tang Numerical Methods for Fourth-Order PDEs
on Overlapping Grids with Application to
Kirchhoff--Love Plates . . . . . . . . . ??
Heping Dong and
Peijun Li A Novel Boundary Integral Formulation
for the Biharmonic Wave Scattering
Problem . . . . . . . . . . . . . . . . ??
Linfeng Xu and
Shengrong Ding and
Kailiang Wu High-Order Accurate Entropy Stable
Schemes for Relativistic Hydrodynamics
with General Synge-Type Equation of
State . . . . . . . . . . . . . . . . . ??
Lingfeng Li and
Xue-Cheng Tai and
Jiang Yang and
Quanhui Zhu A Priori Error Estimate of Deep Mixed
Residual Method for Elliptic PDEs . . . ??
Ali Haidar and
Fabien Marche and
François Vilar Free-Boundary Problems for
Wave--Structure Interactions in
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Local Subcell Correction . . . . . . . . ??
Gang Wang and
Ying Wang Least-Squares Virtual Element Method for
Stokes Problems on Polygonal Meshes . . ??
Weinan Zhang and
Pingping Zeng and
Gongqiu Zhang and
Yue Kuen Kwok Pricing Discretely Monitored Asian
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Stochastic Volatility Models with Jumps ??
Xia Ji and
Yuling Jiao and
Xiliang Lu and
Pengcheng Song and
Fengru Wang Deep Ritz Method for Elliptical Multiple
Eigenvalue Problems . . . . . . . . . . ??
Guixian Xu and
Huihui Wang and
Qingping Zhou Enhancing Electrical Impedance
Tomography Reconstruction Using Learned
Half-Quadratic Splitting Networks with
Anderson Acceleration . . . . . . . . . ??
Han Zhou and
Wenyi Tian Crank--Nicolson Schemes for
Sub-Diffusion Equations with Nonsingular
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Bikram Bir and
Deepjyoti Goswami and
Amiya K. Pani Optimal Error Estimates of the Penalty
Finite Element Method for the Unsteady
Navier--Stokes Equations with Nonsmooth
Initial Data . . . . . . . . . . . . . . ??
Wasilij Barsukow and
Raul Borsche Implicit Active Flux Methods for Linear
Advection . . . . . . . . . . . . . . . ??
Sarvesh Kumar and
David Mora and
Ricardo Ruiz-Baier and
Nitesh Verma Numerical Solution of the
Biot/Elasticity Interface Problem Using
Virtual Element Methods . . . . . . . . ??
Chengtao An and
Yangfeng Su An Aggregation-Based Two-Grid Method for
Multilevel Block Toeplitz Linear Systems ??
Haibo Li Double Precision is not Necessary for
LSQR for Solving Discrete Linear
Ill-Posed Problems . . . . . . . . . . . ??
Aniruddha Seal and
Srinivasan Natesan and
Suayip Toprakseven A Dimensional-Splitting Weak Galerkin
Finite Element Method for 2D
Time-Fractional Diffusion Equation . . . ??
Sebastian Neumayer and
Antonia Topalovic Template-Based Image Reconstruction
Facing Different Topologies . . . . . . ??
Pietro Benedusi and
Paola Ferrari and
Marie E. Rognes and
Stefano Serra-Capizzano Modeling Excitable Cells with the EMI
Equations: Spectral Analysis and
Iterative Solution Strategy . . . . . . ??
Boyang Yu and
Yonghai Li and
Jiangguo Liu A Positivity-Preserving and Robust Fast
Solver for Time-Fractional
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Roland Pulch and
Olivier S\`ete The Helmholtz Equation with
Uncertainties in the Wavenumber . . . . ??
Shuyu Ye and
Qiang Ma and
Qinglin Tang and
Junzhi Cui and
Zhihui Li Second-Order Three-Scale Asymptotic
Analysis and Algorithms for Steklov
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Patrick Ersing and
Andrew R. Winters An Entropy Stable Discontinuous Galerkin
Method for the Two-Layer Shallow Water
Equations on Curvilinear Meshes . . . . ??
Tokuhiro Eto A Rapid Numerical Method for the
Mullins--Sekerka Flow with Application
to Contact Angle Problems . . . . . . . ??
Chenxiao Song and
Reiichiro Kawai Sampling and Change of Measure for Monte
Carlo Integration on Simplices . . . . . ??
Jianan Yao and
Baoling Xie and
Jun Lai A Robust and High Precision Algorithm
for Elastic Scattering Problems from
Cornered Domains . . . . . . . . . . . . ??
Barbara Verfürth Higher-Order Finite Element Methods for
the Nonlinear Helmholtz Equation . . . . ??
Lifang Pei and
Yifan Wei and
Chaofeng Zhang and
Jiwei Zhang Convergence and Superconvergence
Analysis of a Nonconforming Finite
Element Variable-Time-Step BDF2 Implicit
Scheme for Linear Reaction--Diffusion
Equations . . . . . . . . . . . . . . . ??
Mengqing Zhai and
Supei Zheng and
Chengzhi Zhang and
Mangmang Jian A New $S$--$M$ Limiter Entropy Stable
Scheme Based on Moving Mesh Method for
Ideal MHD and SWMHD Equations . . . . . ??
Qiyuan Pang and
Haizhao Yang A Distributed Block Chebyshev--Davidson
Algorithm for Parallel Spectral
Clustering . . . . . . . . . . . . . . . ??
Xue Hong and
Jing-Mei Qiu A Conservative Eulerian--Lagrangian
Runge--Kutta Discontinuous Galerkin
Method for Linear Hyperbolic System with
Large Time Stepping . . . . . . . . . . ??