Abstract
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.
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