Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi; Lucia Gastaldi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 2, page 293-305
  • ISSN: 0764-583X

Abstract

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In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L 2 norm for the sequence of discrete operators. These results, together with a general theory introduced by Brezzi, Rappaz and Raviart [8], allow an immediate proof of convergence for the finite element approximation of the time-harmonic Maxwell system.

How to cite

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Boffi, Daniele, and Gastaldi, Lucia. "Edge finite elements for the approximation of Maxwell resolvent operator." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 293-305. <http://eudml.org/doc/245660>.

@article{Boffi2002,
abstract = {In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the $L^2$ norm for the sequence of discrete operators. These results, together with a general theory introduced by Brezzi, Rappaz and Raviart [8], allow an immediate proof of convergence for the finite element approximation of the time-harmonic Maxwell system.},
author = {Boffi, Daniele, Gastaldi, Lucia},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {edge finite elements; time-harmonic Maxwell’s equations; mixed finite elements; time-harmonic Maxwell's equations, mixed finite elements; convergence},
language = {eng},
number = {2},
pages = {293-305},
publisher = {EDP-Sciences},
title = {Edge finite elements for the approximation of Maxwell resolvent operator},
url = {http://eudml.org/doc/245660},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Boffi, Daniele
AU - Gastaldi, Lucia
TI - Edge finite elements for the approximation of Maxwell resolvent operator
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 2
SP - 293
EP - 305
AB - In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the $L^2$ norm for the sequence of discrete operators. These results, together with a general theory introduced by Brezzi, Rappaz and Raviart [8], allow an immediate proof of convergence for the finite element approximation of the time-harmonic Maxwell system.
LA - eng
KW - edge finite elements; time-harmonic Maxwell’s equations; mixed finite elements; time-harmonic Maxwell's equations, mixed finite elements; convergence
UR - http://eudml.org/doc/245660
ER -

References

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