Two-grid stabilized methods for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions

Abstract

In this paper, we consider a two-grid quadratic equal-order stabilized method for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions. Our two-grid stabilized method consists of computing one nonlinear problem on a coarse mesh and then solving a linearization correction problem on a fine mesh. Moreover, the stability and convergence of the present method are derived. Finally, numerical experiments are performed to confirm our theoretical results.