Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint
The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates in L2(J;L2(Ω))-norm and L2(J;H1(Ω))-norm for both the control and coupled state approximations. Suc...
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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/10.1155/2013/302935 |
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| _version_ | 1832565132719292416 |
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| author | Zuliang Lu |
| author_facet | Zuliang Lu |
| author_sort | Zuliang Lu |
| collection | DOAJ |
| description | The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori
error estimates in L2(J;L2(Ω))-norm and L2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results. |
| format | Article |
| id | doaj-art-de580d7eff1f48cab6a87dc232305827 |
| 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-de580d7eff1f48cab6a87dc2323058272025-02-03T01:09:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/302935302935Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control ConstraintZuliang Lu0School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, ChinaThe aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates in L2(J;L2(Ω))-norm and L2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results.http://dx.doi.org/10.1155/2013/302935 |
| spellingShingle | Zuliang Lu Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint Journal of Applied Mathematics |
| title | Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint |
| title_full | Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint |
| title_fullStr | Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint |
| title_full_unstemmed | Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint |
| title_short | Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint |
| title_sort | adaptive semidiscrete finite element methods for semilinear parabolic integrodifferential optimal control problem with control constraint |
| url | http://dx.doi.org/10.1155/2013/302935 |
| work_keys_str_mv | AT zulianglu adaptivesemidiscretefiniteelementmethodsforsemilinearparabolicintegrodifferentialoptimalcontrolproblemwithcontrolconstraint |