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

Published online by Cambridge University Press:  17 April 2013

Cyril Agut  and
Julien Diaz
Cyril Agut
Affiliation:
LMAP, University of Pau, INRIA Project-Team Magique-3D, France. cyril.agut@orange.fr
Julien Diaz
Affiliation:
INRIA Project-Team Magique-3D, LMAP, University of Pau, France
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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.

Keywords

Discontinuous Galerkinpenalization coefficientCFL conditionwave equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 3 , May 2013 , pp. 903 - 932
Copyright
© EDP Sciences, SMAI, 2013

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