New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems
Abstract In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-0994-3 |
| _version_ | 1828857062823559168 |
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| author | Zuliang Lu Hongyan Liu Chunjuan Hou Longzhou Cao |
| author_facet | Zuliang Lu Hongyan Liu Chunjuan Hou Longzhou Cao |
| author_sort | Zuliang Lu |
| collection | DOAJ |
| description | Abstract In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems. |
| first_indexed | 2024-12-13T01:29:35Z |
| format | Article |
| id | doaj.art-85a833d09d3a4d19b06b92a056d4bb41 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T01:29:35Z |
| publishDate | 2016-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-85a833d09d3a4d19b06b92a056d4bb412022-12-22T00:04:03ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-02-012016111710.1186/s13660-016-0994-3New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problemsZuliang Lu0Hongyan Liu1Chunjuan Hou2Longzhou Cao3Key Laboratory of Signal and Information Processing, Chongqing Three Gorges UniversityChongqing Wanzhou Long Bao Middle SchoolHuashang College, Guangdong University of FinanceKey Laboratory of Signal and Information Processing, Chongqing Three Gorges UniversityAbstract In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems.http://link.springer.com/article/10.1186/s13660-016-0994-3residual-based a posteriori error estimatesnonlinear parabolic optimal control problemshp version of finite element method |
| spellingShingle | Zuliang Lu Hongyan Liu Chunjuan Hou Longzhou Cao New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems Journal of Inequalities and Applications residual-based a posteriori error estimates nonlinear parabolic optimal control problems hp version of finite element method |
| title | New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| title_full | New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| title_fullStr | New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| title_full_unstemmed | New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| title_short | New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| title_sort | new a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems |
| topic | residual-based a posteriori error estimates nonlinear parabolic optimal control problems hp version of finite element method |
| url | http://link.springer.com/article/10.1186/s13660-016-0994-3 |
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