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A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

Published online by Cambridge University Press:  03 June 2015

Wanfang Shen ,
Liang Ge ,
Danping Yang  and
Wenbin Liu
Wanfang Shen*
Affiliation:
School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
Liang Ge*
Affiliation:
Shandong Provincial Key Laboratory of Computer Network, Shandong Computer Science Center, Jinan 250014, China
Danping Yang*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, China
Wenbin Liu*
Affiliation:
KBS, University of Kent, Canterbury, CT2 7NF, England
*
Email: wanfangshen@gmail.com
Email: gel@sdas.org
Email: dpyang@math.ecnu.edu.cn
Corresponding author. Email: W.B.Liu@kent.ac.uk
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Abstract

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in H1 and L2 norms. Furthermore some numerical tests are presented to verify the theoretical results.

Keywords

65N3065R20Optimal controllinear parabolic integro-differential equationsoptimality conditionsfinite element methodsa priori error estimate
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 552 - 569
Copyright
Copyright © Global-Science Press 2014

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