New a posteriori error estimates for optimal control problems governed by parabolic integro-differential equations

In this paper, we provide a new a posteriori error analysis for a linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by a variational discretization method. We first define elliptic reconstructions of numerical solutions and then discuss a posteriori error estimates for all variables.