Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems

Abstract

In this paper, we investigate a priori error estimates for the quadratic opti- mal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are ap- proximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k (k≥ 0). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results. AMS subject classifications: 49J20, 65N30