Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems

Abstract

In this paper, finite volume element method is applied to solve the distributed optimal control problems governed by an elliptic equation. We use the method of variational discretization concept to approximate the problems. The optimal order error estimates in $L^2$ and $L^∞$-norm are derived for the state, costate and control variables. The optimal $H^1$ and $W^{1,∞}$-norm error estimates for the state and costate variables are also obtained. Numerical experiments are presented to test the theoretical results.