Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations

This paper extends the reduced basis method for the solution of parametrized optimal control problemspresented in [1] to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discussboth the theoretical properties – with particular emphasis on the stability of the resulting double nestedsaddle-point problems and on aggregated error estimates – and the computational aspects of the method.Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff bodyimmersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity ofthe methodology.