A COVOLUME METHOD BASED ON ROTATED BILINEARS FOR THE GENERALIZED STOKES PROBLEM

We introduce a covolume or marker and cell (MAC) method for approximat ing the generalized Stokes problem on an axiparallel domain. Two grids are needed, the primal grid made up of rectangles and the dual grid o f quadrilaterals. The velocity is approximated by nonconforming rotate d bilinear elements with degrees of freedom at midpoints of rectangula r elements and the pressure by piecewise constants. The error in the v elocity in the H-h(1) norm and the pressure in the L-2 norm are of fir st order, provided that the exact velocity is in H-2 and the exact pre ssure in H-1.