Anisotropic Superconvergence Analysis for the Wilson Nonconforming Element

1 Introduction The Wilson nonconforming element has been widely used in computational mechanics and struc- tural engineering because of its good convergence. In many practical cases, it seems better than the bilinear conforming finite element. This phenomenon causes the great interest of many people who study finite elements. Some papers about the Wilson element have been published which deal with superconvergence. In 6], the superclose property and the global superconvergence are obtained …

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.