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A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

Published online by Cambridge University Press:  28 May 2015

Tianliang Hou ,
Yanping Chen  and
Yunqing Huang
Tianliang Hou*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China
*
Corresponding author.Email address:htlchb@163.com
Corresponding author.Email address:yanpingchen@scnu.edu.cn
Corresponding author.Email address:huangyq@xtu.edu.cn
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Abstract

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Keywords

49J2065N30A posteriori error estimatesquadratic optimal control problemsparabolic equationsmixed finite element methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 439 - 458
Copyright
Copyright © Global Science Press Limited 2011

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