A semi-smooth Newton method for control constrained boundary optimal control of the Navier–Stokes equations Original Research Article

In this paper we study optimal control of the Navier–Stokes equations when the control acts as a pointwise constrained boundary condition of Dirichlet type. The problem is analyzed in the control space View the MathML sourceH001/2, the optimality system and second order sufficient optimality conditions are derived. For the numerical solution we apply a semi-smooth Newton method to a regularized version of the original problem and show convergence properties of the method and of the regularized solutions towards the original one.