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

In this paper, we study the mathematical formulation for an optimalcontrol problem governed by a linear parabolic integro-differentialequation and present the optimality conditions. We then set up itsweak formulation and the finite element approximation scheme. Basedon these we derive the a priori error estimates for its finiteelement approximation both in $H^1$ and $L^2$ norms. Furthermore, some numerical tests are presented toverify the theoretical results.