A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Abstract In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by usi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1729-4 |
| _version_ | 1818215777495416832 |
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| author | Lin Li Zuliang Lu Wei Zhang Fei Huang Yin Yang |
| author_facet | Lin Li Zuliang Lu Wei Zhang Fei Huang Yin Yang |
| author_sort | Lin Li |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain L2(H1)−L2(L2) $L^{2}(H^{1})-L^{2}(L ^{2})$ a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain L2(L2)−L2(L2) $L^{2}(L^{2})-L^{2}(L^{2})$ a posteriori error estimates of the approximation solutions for both the state and the control. |
| first_indexed | 2024-12-12T06:41:28Z |
| format | Article |
| id | doaj.art-f9c26fe8cb1f45ec8b1f1cca752444a6 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-12T06:41:28Z |
| publishDate | 2018-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-f9c26fe8cb1f45ec8b1f1cca752444a62022-12-22T00:34:20ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-06-012018112310.1186/s13660-018-1729-4A posteriori error estimates of spectral method for nonlinear parabolic optimal control problemLin Li0Zuliang Lu1Wei Zhang2Fei Huang3Yin Yang4Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges UniversityKey Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges UniversityKey Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges UniversityKey Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges UniversityHunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan UniversityAbstract In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain L2(H1)−L2(L2) $L^{2}(H^{1})-L^{2}(L ^{2})$ a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain L2(L2)−L2(L2) $L^{2}(L^{2})-L^{2}(L^{2})$ a posteriori error estimates of the approximation solutions for both the state and the control.http://link.springer.com/article/10.1186/s13660-018-1729-4Optimal control problemNonlinear parabolic equationsVariational discretizationSpectral methodA posteriori error estimates |
| spellingShingle | Lin Li Zuliang Lu Wei Zhang Fei Huang Yin Yang A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem Journal of Inequalities and Applications Optimal control problem Nonlinear parabolic equations Variational discretization Spectral method A posteriori error estimates |
| title | A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| title_full | A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| title_fullStr | A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| title_full_unstemmed | A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| title_short | A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| title_sort | posteriori error estimates of spectral method for nonlinear parabolic optimal control problem |
| topic | Optimal control problem Nonlinear parabolic equations Variational discretization Spectral method A posteriori error estimates |
| url | http://link.springer.com/article/10.1186/s13660-018-1729-4 |
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