New high order schemes based on the modified equation technique for solving the wave equation

Cyril Agut 1, 2, * Julien Diaz 1, 2
* Corresponding author
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
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 bilaplacian 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 present a proof of the convergence of the new scheme. Numerical results illustrate the efficiency of the method.
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Submitted on : Monday, July 5, 2010 - 2:23:35 PM
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Cyril Agut, Julien Diaz. New high order schemes based on the modified equation technique for solving the wave equation. [Research Report] RR-7331, INRIA. 2010, pp.34. ⟨inria-00497627⟩

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