  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.
