We introduce a covolume or marker and cell (MAC) method for approximating the generalized Stokes problem on an axiparallel domain. Two grids are needed, the primal grid made up of rectangles and the dual grid of quadrilaterals. The velocity is approximated by nonconforming rotated bilinear elements with degrees of freedom at midpoints of rectangular elements and the pressure by piecewise constants. The error in the velocity in the Hh norm and the pressure in the L2 norm are of first order, provided that the exact velocity is in H2 and the exact pressure in H1.
Chou, So-Hsiang and Kwak, D. Y., "A Covolume Method Based on Rotated Bilinears for the Generalized Stokes Problem" (1998). Mathematics and Statistics Faculty Publications. 11.
SIAM Journal on Numerical Analysis
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