Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes

The convergence analysis of a Morley type rectangular element for the fourth-order elliptic singular perturbation problem is considered. A counterexample is provided to show that the element is not uniformly convergent with respect to the perturbation parameter. A modified finite element approximati...

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Main Authors: Pingli Xie, Meng Hu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/234375
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author Pingli Xie
Meng Hu
author_facet Pingli Xie
Meng Hu
author_sort Pingli Xie
collection DOAJ
description The convergence analysis of a Morley type rectangular element for the fourth-order elliptic singular perturbation problem is considered. A counterexample is provided to show that the element is not uniformly convergent with respect to the perturbation parameter. A modified finite element approximation scheme is used to get convergent results; the corresponding error estimate is presented under anisotropic meshes. Numerical experiments are also carried out to demonstrate the theoretical analysis.
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institution DOAJ
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publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-49cd331bb14e4e33a74e26550ae36d522025-08-20T02:39:23ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/234375234375Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic MeshesPingli Xie0Meng Hu1School of Sciences, Henan University of Technology, Zhengzhou 450001, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaThe convergence analysis of a Morley type rectangular element for the fourth-order elliptic singular perturbation problem is considered. A counterexample is provided to show that the element is not uniformly convergent with respect to the perturbation parameter. A modified finite element approximation scheme is used to get convergent results; the corresponding error estimate is presented under anisotropic meshes. Numerical experiments are also carried out to demonstrate the theoretical analysis.http://dx.doi.org/10.1155/2014/234375
spellingShingle Pingli Xie
Meng Hu
Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
Abstract and Applied Analysis
title Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
title_full Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
title_fullStr Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
title_full_unstemmed Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
title_short Convergence Analysis of Incomplete Biquadratic Rectangular Element for Fourth-Order Singular Perturbation Problem on Anisotropic Meshes
title_sort convergence analysis of incomplete biquadratic rectangular element for fourth order singular perturbation problem on anisotropic meshes
url http://dx.doi.org/10.1155/2014/234375
work_keys_str_mv AT pinglixie convergenceanalysisofincompletebiquadraticrectangularelementforfourthordersingularperturbationproblemonanisotropicmeshes
AT menghu convergenceanalysisofincompletebiquadraticrectangularelementforfourthordersingularperturbationproblemonanisotropicmeshes