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Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

Published online by Cambridge University Press:  28 May 2015

Yuelong Tang  and
Yanping Chen
Yuelong Tang
Affiliation:
Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, Hunan, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
*
Corresponding author. Email Address: yanpingchen@scnu.edu.cn
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Abstract

In this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the L2 projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

Keywords

35B3749J2065N30Superconvergencefinite element methodsoptimal control problemsparabolic equationsinterpolate operator

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 3 , August 2013 , pp. 209 - 227
Copyright
Copyright © Global-Science Press 2013

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