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

Abstract

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

ow con rm the interest of these approaches.