Plane wave discontinuous Galerkin methods: Analysis of the h-version
ESAIM: M2AN, 43 2 (2009) 297-331
Published online: 2009-02-07
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Domain Decomposition Methods in Science and Engineering XXI
T. Betcke, M. J. Gander and J. PhillipsLecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXI 98 577 (2014)
https://doi.org/10.1007/978-3-319-05789-7_55
A Plane-Wave Least-Squares Method for Time-Harmonic Maxwell's Equations in Absorbing Media
Qiya Hu and Long YuanSIAM Journal on Scientific Computing 36 (4) A1937 (2014)
https://doi.org/10.1137/130928509
A local wave tracking strategy for efficiently solving mid- and high-frequency Helmholtz problems
M. Amara, S. Chaudhry, J. Diaz, R. Djellouli and S.L. FiedlerComputer Methods in Applied Mechanics and Engineering 276 473 (2014)
https://doi.org/10.1016/j.cma.2014.03.012
On Trefftz and weak Trefftz discontinuous Galerkin approaches for medium-frequency acoustics
Pierre Ladevèze and Hervé RiouComputer Methods in Applied Mechanics and Engineering 278 729 (2014)
https://doi.org/10.1016/j.cma.2014.05.024
Dispersion analysis of plane wave discontinuous Galerkin methods
Claude J. Gittelson and Ralf HiptmairInternational Journal for Numerical Methods in Engineering 98 (5) 313 (2014)
https://doi.org/10.1002/nme.4626
A comparison of techniques for overcoming non‐uniqueness of boundary integral equations for the collocation partition of unity method in two‐dimensional acoustic scattering
G.C. Diwan, J. Trevelyan and G. CoatesInternational Journal for Numerical Methods in Engineering 96 (10) 645 (2013)
https://doi.org/10.1002/nme.4583
Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
Lingxue Zhu and Haijun WuSIAM Journal on Numerical Analysis 51 (3) 1828 (2013)
https://doi.org/10.1137/120874643
Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell’s equations on Cartesian grids
Eric T. Chung, Patrick Ciarlet and Tang Fei YuJournal of Computational Physics 235 14 (2013)
https://doi.org/10.1016/j.jcp.2012.10.019
Improvements for the ultra weak variational formulation
T. Luostari, T. Huttunen and P. MonkInternational Journal for Numerical Methods in Engineering 94 (6) 598 (2013)
https://doi.org/10.1002/nme.4469
General DG-Methods for Highly Indefinite Helmholtz Problems
J. M. Melenk, A. Parsania and S. SauterJournal of Scientific Computing 57 (3) 536 (2013)
https://doi.org/10.1007/s10915-013-9726-8
Numerical Mathematics and Advanced Applications 2011
V. Gyrya and K. LipnikovNumerical Mathematics and Advanced Applications 2011 429 (2013)
https://doi.org/10.1007/978-3-642-33134-3_46
DG and hp‐DG for highly indefinite Helmholtz problems
Jens Markus Melenk, Asieh Parsania and Stefan SauterPAMM 13 (1) 443 (2013)
https://doi.org/10.1002/pamm.201310215
M-ADAPTATION METHOD FOR ACOUSTIC WAVE EQUATION ON SQUARE MESHES
VITALIY GYRYA and KONSTANTIN LIPNIKOVJournal of Computational Acoustics 20 (04) 1250022 (2012)
https://doi.org/10.1142/S0218396X12500221
The Ultra Weak Variational Formulation Using Bessel Basis Functions
Teemu Luostari, Tomi Huttunen and Peter MonkCommunications in Computational Physics 11 (2) 400 (2012)
https://doi.org/10.4208/cicp.121209.040111s
On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method
Fengyan LiJournal of Scientific Computing 51 (1) 213 (2012)
https://doi.org/10.1007/s10915-011-9503-5
Overview of the discontinuous enrichment method, the ultra‐weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons
Dalei Wang, Radek Tezaur, Jari Toivanen and Charbel FarhatInternational Journal for Numerical Methods in Engineering 89 (4) 403 (2012)
https://doi.org/10.1002/nme.3239
A stable discontinuous Galerkin-type method for solving efficiently Helmholtz problems
Mohamed Amara, Henri Calandra, Rabia Dejllouli and Magdalena Grigoroscuta-StrugaruComputers & Structures 106-107 258 (2012)
https://doi.org/10.1016/j.compstruc.2012.05.007
Numerical Analysis of Multiscale Problems
S. Esterhazy and J. M. MelenkLecture Notes in Computational Science and Engineering, Numerical Analysis of Multiscale Problems 83 285 (2012)
https://doi.org/10.1007/978-3-642-22061-6_9
Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
Ralf Hiptmair, Andrea Moiola and Ilaria PerugiaMathematics of Computation 82 (281) 247 (2012)
https://doi.org/10.1090/S0025-5718-2012-02627-5
Plane wave approximation of homogeneous Helmholtz solutions
A. Moiola, R. Hiptmair and I. PerugiaZeitschrift für angewandte Mathematik und Physik 62 (5) 809 (2011)
https://doi.org/10.1007/s00033-011-0147-y
Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations
Wei Guo, Fengyan Li and Jianxian QiuJournal of Scientific Computing 47 (2) 239 (2011)
https://doi.org/10.1007/s10915-010-9434-6
Vekua theory for the Helmholtz operator
A. Moiola, R. Hiptmair and I. PerugiaZeitschrift für angewandte Mathematik und Physik 62 (5) 779 (2011)
https://doi.org/10.1007/s00033-011-0142-3
Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension
Jelena Popovic and Olof RunborgBIT Numerical Mathematics 51 (3) 721 (2011)
https://doi.org/10.1007/s10543-011-0315-7
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
R. Hiptmair, A. Moiola and I. PerugiaSIAM Journal on Numerical Analysis 49 (1) 264 (2011)
https://doi.org/10.1137/090761057
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
J. M. Melenk and S. SauterSIAM Journal on Numerical Analysis 49 (3) 1210 (2011)
https://doi.org/10.1137/090776202
A comparison of wave‐based discontinuous Galerkin, ultra‐weak and least‐square methods for wave problems
G. Gabard, P. Gamallo and T. HuttunenInternational Journal for Numerical Methods in Engineering 85 (3) 380 (2011)
https://doi.org/10.1002/nme.2979
Smoothed aggregation for Helmholtz problems
Luke N. Olson and Jacob B. SchroderNumerical Linear Algebra with Applications 17 (2-3) 361 (2010)
https://doi.org/10.1002/nla.686
A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates
S. Britt, S. Tsynkov and E. TurkelJournal of Scientific Computing 45 (1-3) 26 (2010)
https://doi.org/10.1007/s10915-010-9348-3
Domain Decomposition Methods in Science and Engineering XVIII
Ralf Hiptmair and Ilaria PerugiaLecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XVIII 70 51 (2009)
https://doi.org/10.1007/978-3-642-02677-5_5