A posteriori error estimates of mixed methods for quadratic optimal control problems governed by integro-differential equations

This goal of this paper is to study a posteriori error estimates of mixed finite element methods for quadratic optimal control problems governed by integro-differential equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is discretized by piecewise constant elements. We derive a posteriori error estimates for the coupled state and control approximation.