Anisotropic Superconvergence Analysis for the Wilson Nonconforming Element

The regular condition (there exists a constant c independent of the element K and the mesh such that hK/ρK ≤ c, where hK and ρK are diameters of K and the biggest ball contained in K, respectively) or the quasi-uniform condition is a basic assumption in the analysis of classical finite elements. In this paper, the supercloseness for consistency error and the superconvergence estimate at the central point of the element for the Wilson nonconforming element in solving second-order elliptic boundary value problem are given without the above assumption on the meshes. Furthermore the global superconvergence for the Wilson nonconforming element is obtained under the anisotropic meshes. Lastly, a numerical test is carried out which confirms our theoretical analysis.