Stability Analysis for Discontinuous Galerkin approximations of the elastodynamics problem

Paola F. Antonietti, Blanca Ayuso de Dios, Ilario Mazzieri, Alfio Quarteroni

Published 2013-10-30Version 1

We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both {\it displacement} and {\it displacement-stress} formulations. We present the stability analysis of all the methods in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We include some numerical experiments in three dimensions to verify the theory.