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

摘要

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 = 1 Raviart-Thomas mixed finite elements and the control is approximated by piecewise constant functions. We obtain the superconvergence property between average L~2 projection and the approximation of the control variable, and the convergence order is h~2. Two numerical examples are presented for illustrating the superconvergence results.