Analyses of Mixed Continuous and Discontinuous Galerkin Methods for the tIme Harmonic Elasticity Problem with Reduced Symmetry

Abstract

Our purpose is to analyze mixed continuous and discontinuous Galerkin discretizations of the time harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. Under appropriate conditions on the wave number $\kappa$ and the mesh size $h$, we prove asymptotic stability of the continuous and discontinuous Galerkin schemes uniformly in $h$, $\kappa$, and the Lamé coefficient $\lambda$. We also derive for each scheme optimal a priori error bounds in the energy norm. Several numerical tests are presented in order to illustrate the performance of the methods and confirm the theoretical results.