Superconvergence of a modified weak Galerkin approximation for second order elliptic problems by L2 projection method

This paper derives a superconvergence result for the modified weak Galerkin (MWG) finite element method of the second order elliptic problem. The convergence rate of the MWG approximation is improved by 30% after applying a low cost L2 projection post-processing technique. These superconvergence phenomena are proved theoretically and confirmed numerically.