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Variational discretization and mixed methods for semilinear parabolic optimal control problems with integral constraint

Document Type : Research Paper

Author

School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, P.R.China; College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, P.R.China

Abstract

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state and the control variable. As a result, it can be proved that the discrete solutions possess the convergence property of order. Finally, a numerical example is presented which confirms the theoretical results.

Graphical Abstract

Variational discretization and mixed methods for semilinear parabolic optimal control problems with integral constraint

Keywords

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References
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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)
Volume 1, Issue 1 - Serial Number 1
December 2011
Pages 29-36
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