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An arbitrary high order discontinuous Galerkin scheme for the elastodynamic equations

Abstract : We present in this paper the formulation of a non-dissipative arbitrary high order time domain scheme for the elastodynamic equations. Our approach combines the use of an arbitrary high order discontinuous Galerkin interpolation with centred flux in space, with an arbitrary high order leapfrog scheme in time. Numerical two dimensionnal results are presented for the schemes from order two to order four. In these simulations, we discuss of the numerical stability and the numerical convergence of the schemes on the homogeneous eigenmode problem. We also show the ability of the computed schemes to carry out more complex propagation probems by simulating the Garvin test with an explosive source. The results show the high accuracy of the method, both on triangular regular and irregular meshes.
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Serge Moto Mpong. An arbitrary high order discontinuous Galerkin scheme for the elastodynamic equations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2014, 17, pp.93-117. ⟨hal-01300061⟩

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