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A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems

Published online by Cambridge University Press:  28 May 2015

Zuliang Lu*
Affiliation:
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000 and College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, P.R. China.
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
Weishan Zheng*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
*
Corresponding author. Email: zulianglux@126.com
Corresponding author. Email: yanpingchen@scnu.edu.cn
Corresponding author. Email: haohan9@126.com
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Abstract

A Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.

Type
Research Article
Copyright
Copyright © Global-Science Press 2012

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