A posteriori error estimates of variational discretization mixed finite element methods for integro-differential optimal control problem

Abstract

In this paper we study a posteriori error estimates of all discretization parameters for quadratic convex optimal control problems governed by integro-differential equations by using the variational discretization mixed finite element methods. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not approximated. By applying some error estimates results of mixed finite element methods for integro-differential equations, we derive a posteriori error estimates both for the coupled state and the control approximation of the optimal control problem.