Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes (Journal of Computational Mathematics, 2005)
Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to present a novel approach of dealing with the approximation of a four-degree nonconforming finite element for the second order elliptic problems on the anisotropic meshes. The optimal error estimates of energy norm and $L^{2}$-norm without the regular assumption or quasi-uniform assumption are obtained based on some new special features of this element discovered herein. Numerical results are given to demonstrate validity of our theoretical analysis.
Keywords: Anisotropic mesh; Nonconforming finite element; Optimal estimate.