Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

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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Main Author: Zuliang Lu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/302935
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spelling doaj-de580d7eff1f48cab6a87dc2323058272020-11-24T22:35:57ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Zuliang Lu
spellingShingle Zuliang Lu
Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint
Journal of Applied Mathematics
author_facet Zuliang Lu
author_sort Zuliang Lu
title 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_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_sort adaptive semidiscrete finite element methods for semilinear parabolic integrodifferential optimal control problem with control constraint
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/302935
work_keys_str_mv AT zulianglu adaptivesemidiscretefiniteelementmethodsforsemilinearparabolicintegrodifferentialoptimalcontrolproblemwithcontrolconstraint
_version_ 1725721973739225088

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