A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems
Year: 2014
Author: Wanfang Shen, Liang Ge, Danping Yang, Wenbin Liu
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 552–569
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 $H^1$ and $L^2$ norms. Furthermore, some numerical tests are presented to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2012.m30
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 552–569
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Optimal control linear parabolic integro-differential equations optimality conditions finite element methods a priori error estimate.
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