We prove in this paper the convergence of the Marker and Cell (MAC) scheme
for the discretization of the steady state compressible and isentropic
Navier-Stokes equations on two or three-dimensional Cartesian grids. Existence
of a solution to the scheme is proven, followed by estimates on approximate
solutions, which yield the convergence of the approximate solutions, up to a
subsequence, and in an appropriate sense. We then prove that the limit of the
approximate solutions satisfies the mass and momentum balance equations, as
well as the equation of state, which is the main difficulty of this study