Numerical treatment of the Navier-Stokes equations with slip boundary condition

In this article we present efficient numerical methods for the Navier--Stokes equations with slip boundary conditions. A first method is based on a saddle-point formulation of the slip boundary condition. A congruent gradient (CG) method is applied to the Schur complement operator in order to solve the problem. We present two preconditioners for the CG-method which result in convergence rates independent of the mesh size. For a second method the slip boundary condition is enforced pointwise for nodal values of the velocity at boundary nodes.