Whitney Forms of Higher Degree

Francesca Rapetti (1) , Alain Bossavit (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LGEP - Laboratoire de génie électrique de Paris

Low-order Whitney elements are widely used for electromagnetic field problems. Higher-order approximations are receiving increasing interest, but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to p-chains. We provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom. Properties of the higher-order Whitney complex are deeply investigated.

Francesca Rapetti, Alain Bossavit. Whitney Forms of Higher Degree. SIAM Journal on Numerical Analysis, 2009, 47 (3), pp.2369-2386. ⟨10.1137/070705489⟩. ⟨hal-00763881⟩