A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

Abstract

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant func- tions. We derive a posteriori error estimates for both the state and the control approx- imation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approxima- tion schemes for the control problem.