Some remarks on spanning families and weights for high order Whitney spaces on simplices. (1st November 2019)

• Record Type: Journal Article
• Authors: Alonso Rodríguez, Ana; Rapetti, Francesca
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 9(2019)
• Page Start: 2961
• Page End: 2972
• Publication Date: 2019-11-01
• Subjects: High order Whitney forms on simplices -- Spanning family -- Field reconstruction -- New degrees of freedom; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.03.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.