Variational discretization combined with fully discrete splitting positive definite mixed finite elements for parabolic optimal control problems

In this paper, we consider a variational discretization combined with fully discrete splitting positive definite mixed finite element approximation of parabolic optimal control problems. For the state and co-state, Raviart-Thomas mixed finite element spaces and backward Euler scheme are used for space and time discretization, respectively. The variational discretization technique is used for the approximation of the control variable. We derive a priori error estimates for the control, state, and co-state. A numerical example is presented to demonstrate the theoretical results.