A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d-dimension (d= 2 , 3). This method uses polynomials of degree k+ 1 for the stress and of degree k for the displacement (k≥ 0). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any k≥ 0 , the H(div) -like error estimate for the stress and L² error estimate for the displacement are optimal. We further establish the optimal L² error estimate for the stress provided that the Pk+2-Pk+1-1 Stokes pair is stable and k≥ d. We also provide numerical results of MDG showing that the orders of convergence are actually sharp.