Superconvergence of triangular mixed finite elements for optimal control problems with an integral constraint

In this paper, we shall investigate the superconvergence property of quadratic elliptical optimal control problems by triangular mixed finite element methods. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite elements and the control is discretized by piecewise constant functions. We prove the superconvergence error estimate of h2 in L2-norm between the approximated solution and the interpolation of the exact control variable. Moreover, by postprocessing technique, we find that the projection of the discrete adjoint state is superclose (in order h2) to the exact control variable.