Penalty finite element method for Navier-Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for NavierStokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright (C) 2011 John Wiley & Sons, Ltd.