High order edge elements on simplicial meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, p. 1001-1020

Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex. In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one. We give a geometrical localization of all degrees of freedom over particular edges and provide a basis for these elements on simplicial meshes. As for Whitney edge elements of degree one, the basis is expressed only in terms of the barycentric coordinates of the simplex.

DOI : https://doi.org/10.1051/m2an:2007049
Classification:  78M10,  65N30,  68U20
Keywords: Maxwell equations, higher order edge elements, simplicial meshes
@article{M2AN_2007__41_6_1001_0,
     author = {Rapetti, Francesca},
     title = {High order edge elements on simplicial meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {6},
     year = {2007},
     pages = {1001-1020},
     doi = {10.1051/m2an:2007049},
     zbl = {1141.78014},
     mrnumber = {2377104},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_6_1001_0}
}
Rapetti, Francesca. High order edge elements on simplicial meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, pp. 1001-1020. doi : 10.1051/m2an:2007049. http://www.numdam.org/item/M2AN_2007__41_6_1001_0/

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