A nonconforming scheme to solve the parabolic problem

The convergence order O(h2) of the Wilson nonconforming element has been derived by the superconvergence methods so far. In this paper, a nonconforming semi-discrete scheme is derived by the discontinuous Galerkin method when using the Wilson element approximation of the parabolic problem. In the new scheme, the penalty parameter is accurately estimated and the consistency error vanishes. Therefore, the error estimate can only be determined by the interpolation error of which the convergence order is O(h2).