Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis 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 verify our theoretical estimates on two and three dimensions test problems.

Subjects

discontinuous Galerkin methods

elastodynamics equation

stability and error analysis

DDC Class

510: Mathematik

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Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem