High order edge elements on simplicial meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 6, pp. 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
Mots clés : 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},
     pages = {1001--1020},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {6},
     year = {2007},
     doi = {10.1051/m2an:2007049},
     zbl = {1141.78014},
     mrnumber = {2377104},
     language = {en},
     url = {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, Tome 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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