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Beyond pressure stabilization: A low‐order local projection method for the Oseen equation
Author(s) -
Barrenechea Gabriel R.,
Valentin Frédéric
Publication year - 2010
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.3075
Subject(s) - finite element method , projection (relational algebra) , context (archaeology) , property (philosophy) , galerkin method , element (criminal law) , mathematics , projection method , discontinuous galerkin method , work (physics) , vector field , boundary (topology) , mathematical analysis , order (exchange) , mathematical optimization , algorithm , dykstra's projection algorithm , geometry , engineering , structural engineering , geology , mechanical engineering , paleontology , philosophy , epistemology , finance , political science , law , economics
This work proposes a new local projection stabilized finite element method (LPS) for the Oseen problem. The method adds to the Galerkin formulation new fluctuation terms that are symmetric and easily computable at the element level. Proposed for the pair ℙ 1 /ℙ l , l = 0, 1, when the pressure is continuously or discontinuously approximated, well‐posedness and error optimality are proved. In addition, we introduce a cheap strategy to recover an element‐wise mass conservative velocity field in the discontinuous pressure case, a property usually neglected in the stabilized finite element context. Numerics validate the theoretical results and show that the present method improves accuracy to represent boundary layers when compared with alternative approaches. Copyright © 2010 John Wiley & Sons, Ltd.