Optimization techniques for mixed finite element methods of an semilinear elliptic PDEs - superconvergence

Abstract

In this paper, we shall investigate the superconvergence property of semilinear quadratic elliptic optimal control problems by triangular mixed finite element methods. The state and co-state are approximated by Raviart-Thomas mixed finite element spaces of order k, and the control is approximated by piecewise constant functions. We derive the superconvergence properties for both the control variable and the state variables.