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magnetohydrodynamics.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
Jean Luc Guermond, Peter D. Minev
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 36 / Issue 3 / May 2002

Published online by Cambridge University Press:

15 August 2002, pp. 517-536

Print publication:

May 2002
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We show that the Maxwell equations in the low frequency limit, in a domain composed of insulatingand conducting regions, has a saddle point structure, wherethe electric field in the insulating region is the Lagrangemultiplier that enforces the curl-free constraint on the magnetic field.We propose a mixed finite element techniquefor solving this problem, and we show that, under mild regularityassumption on the data, Lagrange finite elements can be usedas an alternative to edge elements.