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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.
@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 },
pages = {1001--1020},
publisher = {EDP-Sciences},
volume = {41},
number = {6},
year = {2007},
doi = {10.1051/m2an:2007049},
mrnumber = {2377104},
zbl = {1141.78014},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007049/}
}
TY - JOUR AU - Rapetti, Francesca TI - High order edge elements on simplicial meshes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2007 SP - 1001 EP - 1020 VL - 41 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007049/ DO - 10.1051/m2an:2007049 LA - en ID - M2AN_2007__41_6_1001_0 ER -
%0 Journal Article %A Rapetti, Francesca %T High order edge elements on simplicial meshes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2007 %P 1001-1020 %V 41 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007049/ %R 10.1051/m2an:2007049 %G en %F M2AN_2007__41_6_1001_0
Rapetti, Francesca. High order edge elements on simplicial meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 6, pp. 1001-1020. doi: 10.1051/m2an:2007049
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