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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.
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https://hal.inria.fr/hal-01109424
Contributor : Nathalie Glinsky Connect in order to contact the contributor
Submitted on : Monday, January 26, 2015 - 12:24:52 PM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM

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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, 2015, 49 (4), pp.1085-1126. ⟨10.1051/m2an/2015001⟩. ⟨hal-01109424⟩

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