ADAPTIVE QUADRILATERAL AND HEXAHEDRAL FINITE ELEMENT METHODS WITH HANGING NODES AND CONVERGENCE ANALYSIS

被引：8
|
作者：
Zhao, Xuying [1 ,2 ]
Mao, Shipeng [1 ]
Shi, Zliong-Ci [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 05期
关键词：
Finite element method; Adaptive algorithm; Hanging node; 1-irregular mesh; Convergence analysis;
D O I：
10.4208/jcm.1001-m3006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the convergence of adaptive finite element methods for the general non-affine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and Boiler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic partial equations is proved. Our analysis is effective for all conforming Q(m) elements which covers both the two- and three-dimensional cases in a unified fashion.
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页码：621 / 644
页数：24
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