Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes

Authors

  • Dong-Yang Shi, Shao-Chun Chen & Ichiro Hagiwara

Keywords:

Anisotropic mesh, Nonconforming finite element, Optimal estimate.

Abstract

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.

Published

2005-08-02

Issue

Section

Articles