A priori error estimates of mixed methods for quadratic convex optimal control problem governed by nonlinear parabolic equations

Abstract

In this paper we investigate a priori error estimates of quadratic convex optimal control problem governed by nonlinear parabolic equations using mixed finite element methods. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. By applying some error estimates results of mixed finite element methods for parabolic equations, we derive a priori error estimates of optimal order both for the coupled state and the control approximation of the optimal control problem.