Superconvergence of triangular Raviart–Thomas mixed finite element methods for a bilinear constrained optimal control problem

In this paper, we analyze the superconvergence of the bilinear constrained elliptic optimal control problem by triangular Raviart–Thomas mixed finite element methods. The state and the co-state are approximated by the order k=1k=1 Raviart–Thomas mixed finite elements and the control is approximated by piecewise constant functions. We obtain the superconvergence property between average L2L2 projection and the approximation of the control variable, and the convergence order is h2h2. Two numerical examples are presented for illustrating the superconvergence results.