TY - JOUR T1 - Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes JO - Journal of Computational Mathematics VL - 4 SP - 373 EP - 382 PY - 2005 DA - 2005/08 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8823.html KW - Anisotropic mesh, Nonconforming finite element, Optimal estimate. AB -
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.