Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems

Abdelaâziz Ezziani 1, 2, * Patrick Joly 3, *
* Corresponding author
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We present a new non conforming space-time mesh refinement method for symmetric first order hyperbolic system. This method is based on the one hand on the use of a conservative higher order discontinuous Galerkin approximation for space discretization and a finite difference scheme in time, on the other hand on appropriate discrete transmission conditions between the grids. We use a discrete energy technique to drive the construction of the matching procedure between the grids and guarantee the stability of the method.
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Abdelaâziz Ezziani, Patrick Joly. Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems. Journal of Computational and Applied Mathematics, Elsevier, 2008. ⟨inria-00339912⟩

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