Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case
Guermond, Jean Luc ; Minev, Peter D.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002), p. 517-536 / Harvested from Numdam
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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.

Publié le : 2002-01-01
DOI : https://doi.org/10.1051/m2an:2002024
Classification:  65N35,  65N25,  65F05,  35J05 
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     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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {36},
     year = {2002},
     pages = {517-536},
     doi = {10.1051/m2an:2002024},
     mrnumber = {1918943},
     zbl = {1137.65437},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2002__36_3_517_0}
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Guermond, Jean Luc; 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, Tome 36 (2002) pp. 517-536. doi : 10.1051/m2an:2002024. http://gdmltest.u-ga.fr/item/M2AN_2002__36_3_517_0/

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