Preconditioning for boundary control problems in fluid dynamics

In recent years, several preconditioning strategies have been proposed for control problems in fluid dynamics. These are a special case of the general saddle point problem in optimisation. Here, we will extend a preconditionier for distributed Stokes control problems, developed by Rees and Wathen, to the case of boundary control. We will show the usefulness of low-rank structures in constructing a good approximation for the Schur complement of the saddle point matrix. In the end, we will discuss the applicability of this strategy for Navier-Stokes control.