Recovery type a posteriori error estimate for distributed convex optimal control problems governed by integral-differential equations

In this paper, we present a recovery type a posteriori error estimate and the superconvergence analysis for the finite element approximation of the distributed convex optimal control problems governed by integral-differential equations. We provide the recovery type a posteriori error estimates for both the control and the state approximation, which is equivalent to the exact error generally. Under some strong conditions, it is not only equivalent, but also asymptotically exact.