A priori error estimates of variational discretization and semi-discrete mixed methods for general parabolic optimal control problems

In this paper we study a priori error estimates of variational discretization and semi-discrete mixed finite element methods for general optimal control problem governed by parabolic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Then, we derive a priori error estimates for the coupled state and the control approximation of the optimal control problem. Finally, we present a numerical example which confirms our theoretical results.