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Analysis and convergence of a MAC‐like scheme for the generalized Stokes problem
Author(s) -
Chou S. H.,
Kwak D. Y.
Publication year - 1997
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199703)13:2<147::aid-num2>3.0.co;2-p
Subject(s) - mathematics , discretization , piecewise , stokes problem , norm (philosophy) , mathematical analysis , partition (number theory) , stokes flow , convergence (economics) , constant function , domain (mathematical analysis) , exact solutions in general relativity , finite element method , geometry , flow (mathematics) , combinatorics , physics , political science , law , economics , thermodynamics , economic growth
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. © 1997 John Wiley & Sons, Inc.