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A Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control Problems |
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| Authors: | Yanping Chen Lingli Liu Zuliang Lu |
| Institution: | 1. School of Mathematical Sciences , South China Normal University , Guangzhou, P.R. China yanpingchen@scnu.edu.cn;3. Department of Mathematics, Hunan Key Laboratory for Computation and Simulation in Science and Engineering , Xiangtan University , Xiangtan, P.R. China;4. College of Mathematics and Computer Sciences , Chongqing Three Gorges University , Chongqing, P.R. China |
| Abstract: | In this article, we shall give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results. |
| Keywords: | A posteriori error estimates Fully discrete Mixed finite element methods Optimal control problems Parabolic equations |