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Superconvergence and L∞-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations

Published online by Cambridge University Press:  28 May 2015

Tianliang Hou
Tianliang Hou*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
*
*Corresponding author.Email address:htlchb@163.com
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Abstract

In this paper, we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem. 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 some superconvergence results for the control variable. Moreover, we derive L∞-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 equationsdistributed optimal control problemssuperconvergenceL∞-error estimatesmixed finite element methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 3 , August 2013 , pp. 479 - 498
Copyright
Copyright © Global Science Press Limited 2013

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