Some remarks on spanning families and weights for high order Whitney spaces on simplices

High order Whitney finite element spaces generally lack natural choices of bases but they do have spanning families. In these pages, we recall such a family on simplicial meshes and we prove theoretically its effectiveness. We also comment on some aspects of a new set of degrees of freedom, the so-c...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-11, Vol.78 (9), p.2961-2972
Main Authors: Alonso Rodríguez, Ana, Rapetti, Francesca
Format: Article
Language:English
Subjects:
Discrete functions
Field reconstruction
High order Whitney forms on simplices
Mathematics
New degrees of freedom
Numerical Analysis
Spanning family
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Summary:High order Whitney finite element spaces generally lack natural choices of bases but they do have spanning families. In these pages, we recall such a family on simplicial meshes and we prove theoretically its effectiveness. We also comment on some aspects of a new set of degrees of freedom, the so-called weights on the small simplices, to represent discrete functions in these spaces.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.03.006