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Analysis and convergence of a MAC-like scheme for the generalized Stokes problem. (English) Zbl 0868.76065
Summary: We introduce a MAC-like scheme (a covolume method on rectangular grids) for approximating the generalized Stokes problem on a polygon with sides parallel to the coordinate axes. Two staggered grids are used in the derivation of the discretization. The velocity is approximated by conforming bilinears over rectangular elements, and the pressure by piecewise constants over macro-rectangular elements. The errors in the velocity in the ${H}^{1}$ norm and the pressure in the ${L}^{2}$ norm are shown to be of the first order, provided that the exact velocity is in ${H}^{2}$ and the exact pressure in ${H}^{1}$, and that the partition family of the domain is regular.
##### MSC:
 76M25 Other numerical methods (fluid mechanics) 76D07 Stokes and related (Oseen, etc.) flows