Optimal error estimates for the stokes and Navier-Stokes equations with slip-boundary condition

Abstract

We consider a finite element discretization by the Taylor-Hood element for the stationary Stokes and Navier-Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H1 and L2 norms for the velocity and pressure respectively.