Optimal control of the convection-diffusion equation using stabilized finite element methods

In this paper we analyze discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then-discretize” and “discretize-then-optimize” coincide for the proposed discretization scheme. This allows for a symmetric optimality system on the discrete level and optimal order of convergence.