Analysis and Convergence of the MAC Scheme. I. The Linear Problem

Abstract

The MAC (Marker and Cell) discretization of fluid flow is analysed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard ${\bf H}^1 $ and $L^2 $ norms are given for the velocity and pressure, respectively.