A new approach of superconvergence analysis of nonconforming Wilson finite element for semi-linear parabolic problem

In this paper, the discontinuous Galerkin method (DGM) of nonconforming Wilson element is studied for the semi-linear parabolic problem. The global superconvergence with respect to the mesh size are derived in the modified H1-norm for the semi-discrete scheme and two fully discrete schemes, in which the usual extrapolation and interpolation post-processing approaches are not involved, and the error estimates are one order higher than that of the traditional Galerkin finite element method (FEM). Therefore, the corresponding results in the existing literature are improved. Finally, some numerical results are provided to confirm the theoretical analysis.