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Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

Published online by Cambridge University Press:  03 June 2015

Yanping Chen ,
Tianliang Hou  and
Weishan Zheng
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
Tianliang Hou*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China
Weishan Zheng*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
*
Corresponding author. URL: http: //math.xtu.edu.cn/myphp/math/ypchen/index.htm, Email: yanpingchen@scnu.edu.cn
Email: haohan_9@126.com
Email: htlchb@163.com
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Abstract

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and L∞-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

Keywords

49J2065N30Elliptic equationsoptimal control problemssuperconvergenceerror estimatesmixed finite element methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 6 , December 2012 , pp. 751 - 768
Copyright
Copyright © Global-Science Press 2012

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