A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations

In this paper, we examine the discontinuous Galerkin (DG) finite element approximation to convex distributed optimal control problems governed by linear parabolic equations, where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization. We derive a posteriori error estimates for both the state and the control approximation, assuming only that the underlying mesh in space is nondegenerate. For problems with control constraints of obstacle type, which are the kind most frequently met in applications, further improved error estimates are obtained.