Superconvergence of Discontinuous Galerkin Methods for Elliptic Boundary Value Problems

In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress formulations. Based on this result, some locally postprocess schemes are employed to improve the accuracy of displacement by order min(k + 1, 2) if polynomials of degree k are employed for displacement. Some numerical experiments are carried out to validate the theoretical results.