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.
