Superconvergence of fully discrete rectangular mixed finite element methods of parabolic control problems

Abstract

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic parabolic optimal control problem by using fully discrete mixed finite element methods. The space discretization of the state variable is done using usual mixed finite elements, whereas the time discretization is based on difference methods. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive the superconvergence results for the control and the state approximation. Some numerical examples are presented to confirm the theoretical investigations.