High order edge elements on simplicial meshes

Francesca Rapetti

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 6, page 1001-1020
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Rapetti, Francesca. "High order edge elements on simplicial meshes." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1001-1020. <http://eudml.org/doc/250061>.

@article{Rapetti2007,
abstract = { 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. },
author = {Rapetti, Francesca},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Maxwell equations; higher order edge elements; simplicial meshes.; simplicial meshes},
language = {eng},
month = {12},
number = {6},
pages = {1001-1020},
publisher = {EDP Sciences},
title = {High order edge elements on simplicial meshes},
url = {http://eudml.org/doc/250061},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Rapetti, Francesca
TI - High order edge elements on simplicial meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/12//
PB - EDP Sciences
VL - 41
IS - 6
SP - 1001
EP - 1020
AB - 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.
LA - eng
KW - Maxwell equations; higher order edge elements; simplicial meshes.; simplicial meshes
UR - http://eudml.org/doc/250061
ER -

References

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