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 - <p style="text-align: justify;">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.</p>