A mixed discontinuous Galerkin method for the time harmonic elasticity problem with reduced symmetry

Abstract

The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that the discontinuous Galerkin scheme is well-posed and uniformly stable with respect to the mesh parameter $h$ and the Lamé coefficient $λ$. We also derive optimal a-priori error bounds in the energy norm. Several numerical tests are presented in order to illustrate the performance of the method and confirm the theoretical results.