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The construction of an optimal weakly divergence‐free macroelement
Author(s) -
Ye Xiu,
Hall Charles A.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361307
Subject(s) - divergence (linguistics) , subspace topology , mathematics , basis (linear algebra) , finite element method , basis function , mathematical analysis , a priori and a posteriori , dimension (graph theory) , node (physics) , function (biology) , space (punctuation) , geometry , pure mathematics , physics , computer science , biology , philosophy , linguistics , epistemology , quantum mechanics , evolutionary biology , thermodynamics , operating system
The divergence‐free finite element method (DFFEM) is a method to find an approximate solution of the Navier‐Stokes equations in a divergence‐free space. That is, the continuity equation is satisfied a priori . DFFEM eliminates the pressure from the calculations and reduces significantly the dimension of the system to be solved at each time step. For the standard 8‐node velocity and 4‐node pressure DFFEM, an optimal basis for the weakly divergence‐free subspace is constructed such that each basis function has non‐zero support on at most nine contiguous elements. Given this basis, weakly divergence‐free macroelements are constructed.