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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