TY - JOUR T1 - A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems AU - Shen , Wanfang AU - Ge , Liang AU - Yang , Danping AU - Liu , Wenbin JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 552 EP - 569 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2012.m30 UR - https://global-sci.org/intro/article_detail/aamm/35.html KW - Optimal control, linear parabolic integro-differential equations, optimality conditions, finite element methods, a priori error estimate. AB -

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.