Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation

Cyril Agut; Julien Diaz

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 3, page 903-932
  • ISSN: 0764-583X

Abstract

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We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.

How to cite

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Agut, Cyril, and Diaz, Julien. "Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.3 (2013): 903-932. <http://eudml.org/doc/273286>.

@article{Agut2013,
abstract = {We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.},
author = {Agut, Cyril, Diaz, Julien},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {discontinuous Galerkin; penalization coefficient; CFL condition; wave equation},
language = {eng},
number = {3},
pages = {903-932},
publisher = {EDP-Sciences},
title = {Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation},
url = {http://eudml.org/doc/273286},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Agut, Cyril
AU - Diaz, Julien
TI - Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 3
SP - 903
EP - 932
AB - We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.
LA - eng
KW - discontinuous Galerkin; penalization coefficient; CFL condition; wave equation
UR - http://eudml.org/doc/273286
ER -

References

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