Volume 23, Issue 4
Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes

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

DOI:

J. Comp. Math., 23 (2005), pp. 373-382

Published online: 2005-08

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  • 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.

  • Keywords

Anisotropic mesh Nonconforming finite element Optimal estimate

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@Article{JCM-23-373, author = {}, title = {Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {4}, pages = {373--382}, 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8823.html} }
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://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/8823.html KW - Anisotropic mesh KW - Nonconforming finite element KW - 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.
Dong-Yang Shi, Shao-Chun Chen & Ichiro Hagiwara. (1970). Convergence Analysis for a Nonconforming Membrane Element on Anisotropic Meshes. Journal of Computational Mathematics. 23 (4). 373-382. doi:
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