OPERATOR SPLITTING METHODS FOR THE NAVIER-STOKES EQUATIONS WITH NONLINEAR SLIP BOUNDARY CONDITIONS

In this paper, the theta scheme of operator splitting methods is applied to the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind with the Navier-Stokes operator. Firstly, we introduce the multiplier such that the variational inequality is equivalent to the variational identity. Subsequently, we give the theta scheme to compute the variational identity and consider the finite element approximation of the theta scheme. The stability and convergence of the theta scheme are showed. Finally, we give the numerical results.