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

Ana Alonso Rodríguez (1) , Francesca Rapetti (2, 3)

1 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 CASTOR - Control, Analysis and Simulations for TOkamak Research

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.

Mots clés: New degrees of freedom; High order Whitney forms on simplices; spanning family; field reconstruction; new degrees of freedom 2000 MSC: 65M60; 74J05

Domaines: Analyse numérique [math.NA]

Ana Alonso Rodríguez, Francesca Rapetti. Some remarks on spanning families and weights for high order Whitney spaces on simplices. Computers & Mathematics with Applications, 2019, 78 (9), pp.2961-2972. ⟨10.1016/j.camwa.2019.03.006⟩. ⟨hal-02411192⟩