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A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

Published online by Cambridge University Press:  06 March 2015

Yanping Chen  and
Zhuoqing Lin
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, P.R. China
Zhuoqing Lin
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, P.R. China
*
*Corresponding author. Email addresses: yanpingchen@scnu.edu.cn (Y. Chen), 0626lzq@sina.com (Z. Lin)
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Abstract

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order k, and the control is approximated by piecewise polynomials of order k (k ≥ 0). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Keywords

49J2065N30A posteriori error estimatesoptimal control problemsparabolic equationselliptic reconstructionsemidiscrete mixed finite element methods

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 1 , February 2015 , pp. 85 - 108
Copyright
Copyright © Global-Science Press 2015 

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