  We prove in this paper the convergence of the Marker and cell (MAC) scheme
for the dis-cretization of the steady-state and unsteady-state incompressible
Navier-Stokes equations in primitive variables on non-uniform Cartesian grids,
without any regularity assumption on the solution. A priori estimates on
solutions to the scheme are proven ; they yield the existence of discrete
solutions and the compactness of sequences of solutions obtained with family of
meshes the space step of which tends to zero. We then establish that the limit
is a weak solution to the continuous problem.
