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.
Mots-clés : finite element method, magnetohydrodynamics
@article{M2AN_2002__36_3_517_0,
author = {Guermond, Jean Luc and Minev, Peter D.},
title = {Mixed finite element approximation of an {MHD} problem involving conducting and insulating regions : the {2D} case},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {517--536},
publisher = {EDP-Sciences},
volume = {36},
number = {3},
year = {2002},
doi = {10.1051/m2an:2002024},
mrnumber = {1918943},
zbl = {1137.65437},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2002024/}
}
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: Modélisation mathématique et analyse numérique PY - 2002 SP - 517 EP - 536 VL - 36 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2002024/ DO - 10.1051/m2an:2002024 LA - en ID - M2AN_2002__36_3_517_0 ER -
%0 Journal Article %A Guermond, Jean Luc %A Minev, Peter D. %T Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 517-536 %V 36 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2002024/ %R 10.1051/m2an:2002024 %G en %F M2AN_2002__36_3_517_0
Guermond, Jean Luc; Minev, Peter D. Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 3, pp. 517-536. doi : 10.1051/m2an:2002024. http://archive.numdam.org/articles/10.1051/m2an:2002024/
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