Two-step algorithms for the stationary incompressible Navier-Stokes equations with friction boundary conditions

Two-step algorithms for the stationary incompressible Navier-Stokes equations with friction boundary conditions are considered in this paper. Our algorithms consist of solving one Navier-Stokes variational inequality problem used the linear equal-order finite element pair (i.e., P1-P1) and then solving a linearization variational inequality problem used the quadratic equal-order finite element pair (i.e., P2-P2). Moreover, the stability and convergence of our two-step algorithms are derived. Finally, numerical tests are presented to check theoretical results.