A priori error estimates of mixed finite element methods for nonlinear quadratic convex optimal control problem

Abstract

In this paper, we study an a priori error analysis for the quadratic optimal control problems governed by nonlinear elliptic partial differential equations using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. A priori error estimates for the mixed finite element approximation of nonlinear optimal control problems is obtained. Some numerical examples are presented to confirm our theoretical results.