Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems

In this paper, we investigate the discretization of general convex optimal control problem using the mixed finite element method. The state and co-state are discretized by the lowest order Raviart-Thomas element and the control is approximated by piecewise constant functions. We derive error estimates for both the control and the state approximation. Moreover, we present the superconvergence analysis for mixed finite element approximation of the optimal control problem. Finally, some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence.