(untitled) (Advances in Applied Mathematics and Mechanics, 2014)
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.