Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lame system of linear elasticity in polyhedral domains inxc2xa0mathbb R3. In order to resolve possible corner, edge, and corneredge singularities, anisotropic geometric edge meshes consisting of hexahedral elements are applied. We perform a computational study on the discrete infsup stability of these methods, and especially focus on the robustness with respect to the Poisson ratio close to the incompressible limit (i.e. the Stokes system). Furthermore, under certain realistic assumptions (for analytic data) on the regularity of the exact solution, we illustrate numerically that the proposed mixed DG schemes converge exponentially in a natural DG norm.

A New Hybrid Staggered Discontinuous Galerkin Method on General Meshes A novel highorder hybrid staggered discontinuous Galerkin method for general meshes is proposed to solve general second order elliptic problems. Our new formulation is related to standard staggered discontinuous Galerkin method, but more flexible and cost effective: rough grids are allowed and the size of the final system is remarkably reduced thanks to the partial hybridization. Optimal convergence estimates for both the scalar and vector variables are developed. Moreover, superconvergent results with respect to discrete H1 norm and L2 norm for the scalar variable are proved and negative norm error estimates for both the scalar and vector variables are also developed. On the other hand, mesh adaptation is particularly simple since hanging nodes are allowed, which makes the proposed method well suited for adaptive mesh refinement.  Therefore, we design a residual type a posteriori error estimator, and the reliability and local efficiency of the error estimator are proved. Numerical experiments confirm the theoretical findings.