Variational discretization for optimal control problems governed by parabolic equations

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations. The state and co-state are approximated by Raviart-Thomas mixed finite element spaces, and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. A priori error estimates are derived for the state, the co-state, and the control. Some numerical examples are presented to confirm the theoretical investigations.