ANALYSIS OF A DISCONTINUOUS GALERKIN METHOD FOR ELASTODYNAMIC EQUATIONS. APPLICATION TO 3D WAVE PROPAGATION.

In this paper, we introduce a second-order leap-frog time scheme combined with a high-order discontinuous Galerkin method for the solution of the 3D elastodynamic equations. 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 scheme, and we illustrate the convergence results by the propagation of an eigenmode. Finally, we examine a more realistic 3D test case simulating the propagation of the wave produced by an explosive source in a half-space which constitutes a validation of the source introduction and the absorbing boundary conditions.