A robust finite element method for Darcy-Stokes flow

• 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
• Institution: Nanyang Technological University

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.