Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations

Abstract

In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. A symmetric interior penalty Galerkin method in space and a backward Euler method in time are applied in order to discretize the optimization problem. Numerical results are presented, which illustrate the performance of the proposed error estimators.