A SUPERCONVERGENT L∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT

In this paper, we investigate the superconvergence property of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. A superconvergent approximation of the control variable u will be constructed by a projection of the discrete adjoint state. It is proved that this approximation have convergence order h(2) in L-infinity-norm. Finally, a numerical example is given to demonstrate the theoretical results.