We use in this paper a method described in DINH-GLOWINSKIMANTEL-PERIAUX
, for which we refer for more details for solving the time dependent
Navier-Stokes equations for incompressible viscous fluids. This method
combine finite elements for the space discretization and alternating directions for the time discretization. The use of the splitting associated to the alternating direction method decouples the two main difficulties of the original problem, namely non linearity and incompressibility. However this method is a natural extension of those described in   since least squares and conjugate gradient algorithms
are still the main ingredients used to treat the nonlinearity. Results
of numerical experiments using this technique for the numerical
simulation of the Navier-Stokes flow in a prescribed for analysis
channel with a step are presented.