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

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.

Author Details

Wanfang Shen

Liang Ge

Danping Yang

Wenbin Liu

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