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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*
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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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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
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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
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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
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