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, Volume 36 (2002) no. 3, p. 517-536

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.

DOI : https://doi.org/10.1051/m2an:2002024
Classification:  65N35,  65N25,  65F05,  35J05
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {3},
     year = {2002},
     pages = {517-536},
     doi = {10.1051/m2an:2002024},
     zbl = {1137.65437},
     mrnumber = {1918943},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_3_517_0}
}
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, Volume 36 (2002) no. 3, pp. 517-536. doi : 10.1051/m2an:2002024. http://www.numdam.org/item/M2AN_2002__36_3_517_0/

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