A priori error estimates of finite volume method for nonlinear optimal control problem

Abstract

In this paper, we study a priori error estimates for the finite volume element approximation of nonlinear elliptic and parabolic optimal control problem. The Schemes use discretizations base on a finite volume method. For the variational inequality, we use the method of the variational discretization concept to obtain the control. Under some reasonable assumptions, we obtain some optimal order error estimates. The approximate order for the state, costate and control variables was obtained in the sense of some norms. Some numerical experiments are presented to test the theoretical result. Finally, we give some conclusions and future works.