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Volume 28, Issue 5
Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis

Xuying Zhao, Shipeng Mao & Zhong-Ci Shi

DOI: 10.4208/jcm.1001-m3006

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

Published online: 2010-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N12, 65N15, 65N30, 65N50, 35J25.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-28-621, author = {Xuying Zhao, Shipeng Mao and Zhong-Ci Shi}, title = {Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1001-m3006}, url = {http://global-sci.org/intro/article_detail/jcm/8541.html} }
TY - JOUR T1 - Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis AU - Xuying Zhao, Shipeng Mao & Zhong-Ci Shi JO - Journal of Computational Mathematics VL - 5 SP - 621 EP - 644 PY - 2010 DA - 2010/10 SN - 28 DO - http://doi.org/10.4208/jcm.1001-m3006 UR - https://global-sci.org/intro/article_detail/jcm/8541.html KW - Finite element method, Adaptive algorithm, Hanging node, 1-irregular mesh, Convergence analysis. AB -

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.

Xuying Zhao, Shipeng Mao and Zhong-Ci Shi. (2010). Adaptive Quadrilateral and Hexahedral Finite Element Methods with Hanging Nodes and Convergence Analysis. Journal of Computational Mathematics. 28 (5). 621-644. doi:10.4208/jcm.1001-m3006
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