A posteriori error analysis for finite element approximations of parabolic optimal control problems with measure data

Abstract This paper is concerned with residual type a posteriori error estimates of fully discrete finite element approximations for parabolic optimal control problems with measure data in a bounded convex domain. Two kinds of control problems, namely measure data in space and measure data in time, are considered and analyzed. We use continuous piecewise linear functions for approximations of the state and co-state variables and piecewise constant functions for the control variable. The time discretization is based on the backward Euler implicit scheme. We derive a posteriori error estimates for the state, co-state and control variables in the L 2 ( 0 , T ; L 2 ( Ω ) ) -norm. Finally, numerical tests are presented to illustrate the performance of the estimators.