Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation
1 Universitéde Lyon, CNRS UMR5208,
Université Lyon 1, Institut Camille Jordan, 43 blvd du 11 novembre 1918, 69622
2 UCBL/INRIA Grenoble Rhône-Alpes/INSMI − KALIFFE, France.
3 IFSTTAR/CEREMA, DTer Méd., 56 boulevard Stalingrad, 06359 Nice cedex 4, France.
4 INRIA Sophia Antipolis Méditerranée, team Nachos, 2004 route des Lucioles, 06902 Sophia Antipolis cedex, France.
Revised: 17 October 2014
In this paper, we introduce a high-order discontinuous Galerkin method, based on centered 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.
Mathematics Subject Classification: 35L50 / 35F10 / 35F15 / 35L05 / 35Q99
Key words: Discontinuous Galerkin method / centered flux / leap-frog scheme / elastodynamic equation
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