TY - JOUR
T1 - Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes
AU - Dong-Yang Shi, Shao-Chun Chen & Ichiro Hagiwara
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 - <p style="text-align: justify;">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.</p>