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Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints

Published online by Cambridge University Press:  28 May 2015

Y. Tang  and
Y. Hua
Y. Tang*
Affiliation:
Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, Hunan, China
Y. Hua*
Affiliation:
Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, Hunan, China
*
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
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Abstract

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

Keywords

35B3749J2065N30Superconvergencefinite element methodoptimal control problemsparabolic equationsintegral constraint
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 2 , May 2013 , pp. 138 - 153
Copyright
Copyright © Global-Science Press 2013

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