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Generalizations to discrete and analytical Crouzeix–Velte decompositions
Author(s) -
Stoyan G.,
Strauber G.,
Baran Á.
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.360
Subject(s) - mathematics , boundary value problem , decomposition , finite element method , order (exchange) , element (criminal law) , grid , boundary (topology) , elasticity (physics) , mathematical analysis , boundary values , geometry , thermodynamics , physics , ecology , finance , political science , law , economics , biology
In this paper, the Crouzeix–Velte decomposition is generalized with respect to boundary conditions and boundary value problems, moreover, in the discrete case, the gap between the first‐order staggered grid approximation and the high‐order Scott–Vogelius elements (which was the only finite element family until now for which such a decomposition was known) is filled by proving that the (second‐order) Fortin–Soulie elements also admit such a decomposition—which is of advantage when iteratively solving the corresponding boundary value problems (Stokes, linear elasticity) and for long‐term calculations. Copyright © 2004 John Wiley & Sons, Ltd.