Commun. Comput. Phys., 11 (2012), pp. 691-708.


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

Cyril Agut 1*, Julien Diaz 1, Abdelaaziz Ezziani 1

1 LMA, CNRS UMR 5142, Universite de Pau, France; and INRIA Bordeaux Research Center, Project Team Magique3D, France.

Received 31 December 2009; Accepted (in revised version) 5 November 2010
Available online 24 October 2011
doi:10.4208/cicp.311209.051110s

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.

AMS subject classifications: 65M12, 65M60, 35L05

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Key words: High order schemes, discontinuous Galerkin method, acoustic wave equation.

*Corresponding author.
Email: cyril.agut@univ-pau.fr (C. Agut), julien.diaz@inria.fr (J. Diaz), abdelaaziz.ezziani@univ-pau.fr (A. Ezziani)
 

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