J. Comp. Math., 28 (2010), pp. 621-644.


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

Xuying Zhao 1, Shipeng Mao 2, Zhong-Ci Shi 2

1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Graduate University of Chinese Academy of Sciences, Beijing 100190, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received 2008-12-31 Accepted 2009-11-6
Available online 2010-5-1
doi:10.4208/jcm.1001-m3006

Abstract

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 D\"ofler 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.

Key words: Finite element method, Adaptive algorithm, Hanging node, 1-irregular

AMS subject classifications: 65N12, 65N15, 65N30, 65N50, 35J25


Email: zhaoxy@lsec.cc.ac.cn, maosp@lsec.cc.ac.cn, shi@lsec.cc.ac.cn
 

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