Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case

Jean Luc Guermond; Peter D. Minev

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

  • Volume: 36, Issue: 3, page 517-536
  • ISSN: 0764-583X

Abstract

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We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.

How to cite

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Guermond, Jean Luc, and Minev, Peter D.. "Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.3 (2002): 517-536. <http://eudml.org/doc/245536>.

@article{Guermond2002,
abstract = {We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.},
author = {Guermond, Jean Luc, Minev, Peter D.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element method; magnetohydrodynamics},
language = {eng},
number = {3},
pages = {517-536},
publisher = {EDP-Sciences},
title = {Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case},
url = {http://eudml.org/doc/245536},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Guermond, Jean Luc
AU - Minev, Peter D.
TI - Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 3
SP - 517
EP - 536
AB - We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
LA - eng
KW - finite element method; magnetohydrodynamics
UR - http://eudml.org/doc/245536
ER -

References

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