Stability analysis for Discontinuous Galerkin approximations of the elastodynamics problem

Code:
56/2013
Title:
Stability analysis for Discontinuous Galerkin approximations of the elastodynamics problem
Date:
Friday 15th November 2013
Author(s):
Antonietti, P.F.; Ayuso de Dios, B.; Mazzieri, I.; Quarteroni, A.
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Abstract:
We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both displacement and 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.