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Discrete Dynamics in Nature and Society
Volume 2012, Article ID 481295, 24 pages
Research Article

A Posteriori Error Estimates for a Semidiscrete Parabolic Integrodifferential Control on Multimeshes

School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China

Received 18 August 2012; Accepted 26 September 2012

Academic Editor: Hua Su

Copyright © 2012 Wanfang Shen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We extend the existing techniques to study semidiscrete adaptive finite element approximation schemes for a constrained optimal control problem governed by parabolic integrodifferential equations. The control problem involves time accumulation and the control constrain is given in an integral obstacle sense. We first prove the uniqueness and existence of the solution of this optimal control problem. We then derive the upper a posteriori error estimators for both the state and the control approximation, which are useful indicators in adaptive multimesh finite element approximation schemes.