Divergence free virtual elements for the stokes problem on polygonal meshes

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a...

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Published inESAIM. Mathematical modelling and numerical analysis Vol. 51; no. 2; pp. 509 - 535
Main Authors da Veiga, Lourenco Beirão, Lovadina, Carlo, Vacca, Giuseppe
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.03.2017
Subjects
65N12
65N15
65N30
76D07
Degrees of freedom
Divergence
divergence free approximation
Error analysis
polygonal meshes
Stokes problem
Test procedures
Virtual element method
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Summary:In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with fewer degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.
Bibliography:lourenco.beirao@unimib.it
istex:00AD00F2CAD97EF62096712F9EEDAAC1C236C2B7
publisher-ID:m2an150187
ark:/67375/80W-5FDLVQJC-C
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016032