A robust finite element method for Darcy-Stokes flow

A robust finite element method for Darcy-Stokes flow

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson's equation as the pert...

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Bibliographic Details
Main Authors: Mardal, Kent Andre, Tai, Xue Cheng, Winther, Ragnar
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2009
Subjects:
DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Online Access:https://hdl.handle.net/10356/90843
http://hdl.handle.net/10220/4594
http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=0036-1429&date=2002&volume=40&issue=5&spage=1605&epage=1631&aulast=Mardal&aufirst=%20KA&auinit=KA&title=SIAM%20JOURNAL%20ON%20NUMERICAL%20ANALYSIS&atitle=A%20robust%20finite%20element%20method%20for%20Darcy%2DStokes%20flow
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Institution: Nanyang Technological University
Language: English
Description
Summary:Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of the proposed finite element methods for Stokes problem or the mixed Poisson's system are not well behaved uniformly in the perturbation parameter. This is used as the motivation for introducing a new "robust" finite element which exhibits this property.

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