Error estimates of variational discretization and mixed finite element methods for semilinear parabolic optimal control problems

In this paper we study the variational discretization and mixed finite element methods for optimal control problem governed by semilinear 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. We derive a priori error estimates for the coupled state and the control approximation of the semilinear parabolic optimal control problems. Finally, we present a numerical example which confirms our theoretical results.