Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients
A new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumpti...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/764165 |
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| _version_ | 1832548734657888256 |
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| author | Xiaofei Guan Xiaoling Wang Cheng Wang Xian Liu |
| author_facet | Xiaofei Guan Xiaoling Wang Cheng Wang Xian Liu |
| author_sort | Xiaofei Guan |
| collection | DOAJ |
| description | A new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumption that the oscillating coefficient is periodic, some superconvergence results are derived, which seem to be never discovered in the previous literature. Finally, some numerical experiments are carried out to demonstrate the efficiency and accuracy of this method, and it is seen that they agree very well with the analytical result. |
| format | Article |
| id | doaj-art-78240a53ce0f43f1beddeb93eb20998c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-78240a53ce0f43f1beddeb93eb20998c2025-02-03T06:13:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/764165764165Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating CoefficientsXiaofei Guan0Xiaoling Wang1Cheng Wang2Xian Liu3Department of Mathematics, Tongji University, Shanghai 200092, ChinaDepartment of Fundamental Subject, Tianjin Institute of Urban Construction, Tianjin 300384, ChinaDepartment of Mathematics, Tongji University, Shanghai 200092, ChinaDepartment of Geotechnical Engineering, Tongji University, Shanghai 200092, ChinaA new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumption that the oscillating coefficient is periodic, some superconvergence results are derived, which seem to be never discovered in the previous literature. Finally, some numerical experiments are carried out to demonstrate the efficiency and accuracy of this method, and it is seen that they agree very well with the analytical result.http://dx.doi.org/10.1155/2013/764165 |
| spellingShingle | Xiaofei Guan Xiaoling Wang Cheng Wang Xian Liu Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients Journal of Applied Mathematics |
| title | Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients |
| title_full | Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients |
| title_fullStr | Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients |
| title_full_unstemmed | Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients |
| title_short | Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients |
| title_sort | superconvergence analysis of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients |
| url | http://dx.doi.org/10.1155/2013/764165 |
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