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Analysis and convergence of a MAC-like scheme for the generalized Stokes problem

✍ Scribed by S. H. Chou; D. Y. Kwak

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 157 KB
Volume: 13
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199703)13:2<147::aid-num2>3.0.co;2-p

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✦ Synopsis

We introduce a MAC-like scheme (a covolume method on rectangular grids) for approximating the generalized Stokes problem on an axiparallel domain. 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 error in the velocity in the H 1 norm and the pressure in the L 2 norm are shown to be of 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.

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