$L^∞$-Error Estimates for General Optimal Control Problem by Mixed Finite Element Methods

Abstract

In this paper, we investigate the $L^∞$-error estimates for the solutions of general optimal control problem by 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. We derive $L^∞$-error estimates of optimal order both for the state variables and the control variable.