Numerical methods for the Stokes and Navier-Stokes equations driven by threshold slip boundary conditions

摘要

In this article, we discuss the numerical solution of the Stokes andNavier-Stokes equations completed by nonlinear slip boundary condi-tions of friction type in two and three dimensions. To solve the Stokessystem, we rst reduce the related variational inequality into a saddlepoint-point problem for a well chosen augmented Lagrangian. To solvethis saddle point problem we suggest an alternating direction methodof multiplier together with nite element approximations. The solutionof the Navier Stokes system combines nite element approximations,time discretization by operator splitting and augmented Lagrangianmethod. Numerical experiment results for two and three dimensionalow con rm the interest of these approaches.