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High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation

Published online by Cambridge University Press:  20 August 2015

Cyril Agut ,
Julien Diaz  and
Abdelaâziz Ezziani
Cyril Agut*
Affiliation:
LMA, CNRS UMR 5142, Université de Pau, France INRIA Bordeaux Research Center, Project Team Magique3D, France
Julien Diaz*
Affiliation:
LMA, CNRS UMR 5142, Université de Pau, France INRIA Bordeaux Research Center, Project Team Magique3D, France
Abdelaâziz Ezziani
Affiliation:
LMA, CNRS UMR 5142, Université de Pau, France INRIA Bordeaux Research Center, Project Team Magique3D, France
*
Corresponding author.Email:cyril.agut@univ-pau.fr
Email address:julien.diaz@inria.fr
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Abstract

We present a new high order method in space and time for solving the wave equation, based on a new interpretation of the “Modified Equation” technique. Indeed, contrary to most of the works, we consider the time discretization before the space discretization. After the time discretization, an additional biharmonic operator appears, which can not be discretized by classical finite elements. We propose a new Discontinuous Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.

Keywords

65M1265M6035L05High order schemesdiscontinuous Galerkin methodacoustic wave equation
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 691 - 708
Copyright
Copyright © Global Science Press Limited 2012

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References

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