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Iterative stabilization of the bilinear velocity–constant pressure element
Author(s) -
Fortin M.,
Boivin S.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650100202
Subject(s) - subspace topology , bilinear interpolation , piecewise , finite element method , mathematics , constant (computer programming) , compressibility , work (physics) , piecewise linear function , constant function , element (criminal law) , invariant subspace , mathematical analysis , bandwidth (computing) , iterative method , incompressible flow , mathematical optimization , linear subspace , geometry , computer science , mechanics , physics , law , computer network , statistics , political science , thermodynamics , programming language
Some finite element approximations of incompressible flows, such as those obtained with the bilinear velocity–constant pressure element ( Q 1 − P 0 ), are well known to be unstable in pressure while providing reasonable results for the velocity. We shall see that there exists a subspace of piecewise constant pressures that leads to a stable approximation. The main drawback associated with this subspace is the necessity of assembling groups of elements, the so‐called ‘macro‐elements’, which increases dramatically the bandwidth of the system. We study a variant of Uzawa's method which enables us to work in the desired subspace without increasing the bandwidth of the system. Numerical results show that this method is efficient and can be made to work at a low extra cost. The method can easily be generalized to other problems and is very attractive in three‐dimensional cases.