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Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis

Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis

Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 5 : pp. 621–644

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 Döfler 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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1001-m3006

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 5 : pp. 621–644

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Finite element method Adaptive algorithm Hanging node 1-irregular mesh Convergence analysis.

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