Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation

Abstract : in this paper, we introduce a high-order discontinuous Galerkin method, based on centerd fluxes and a family of high-order leap-frog time schemes, for the solution of the 3D elastodynamic equations written in velocity-stress formulation. We prove that this explicit scheme is stable under a CFL type condition obtained from a discrete energy which is preserved in domains with free surface or decreasing in domains with absorbing boundary conditions. Moreover, we study the convergence of the method for both the semi-discrete and the fully discrete schemes and we illustrate the convergence results by the propagation of an eigenmode. We also propose a series of absorbing conditions which allow improving the convergence of the global scheme. Finally, several numerical applications of wave propagation, using a 3D solver, help illustrating the various properties of the method.
Type de document :
Article dans une revue
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, pp.42
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https://hal.inria.fr/hal-01109424
Contributeur : Nathalie Glinsky <>
Soumis le : lundi 26 janvier 2015 - 12:24:52
Dernière modification le : jeudi 3 mai 2018 - 13:32:55

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  • HAL Id : hal-01109424, version 1

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Sarah Delcourte, Nathalie Glinsky. Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, pp.42. 〈hal-01109424〉

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