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Error Estimates and Superconvergence of RT0 Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems

Published online by Cambridge University Press:  28 May 2015

Yanping Chen and
Tianliang Hou
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
Tianliang Hou*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, ChinaResearch Institute of Hong Kong Baptist University in Shenzhen, Shenzhen 518057, Guangdong, China
*
Corresponding author.Email address:yanpingchen@scnu.edu.cn
Corresponding author.Email address:htlchb@163.com
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Abstract

In this paper, we will investigate the error estimates and the superconvergence property of mixed finite element methods for a semilinear elliptic control problem with an integral constraint on control. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element and the control variable is approximated by piecewise constant functions. We derive some superconvergence properties for the control variable and the state variables. Moreover, we derive L∞- and H−1 -error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

Keywords

49J2065N30Semilinear elliptic equationsoptimal control problemssuperconvergenceerror estimatesmixed finite element methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 4 , November 2013, pp. 637 - 656
Copyright
Copyright © Global Science Press Limited 2013

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