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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/234375 |
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| _version_ | 1850104134749913088 |
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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. |
| format | Article |
| id | doaj-art-49cd331bb14e4e33a74e26550ae36d52 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |