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

Published online by Cambridge University Press:  15 August 2002

Jean Luc Guermond  and
Peter D. Minev
Jean Luc Guermond
Affiliation:
LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. [email protected].
Peter D. Minev
Affiliation:
Department of Mathematical Sciences, University of Alberta Edmonton, Alberta, Canada T6G 2G1, Canada. [email protected].
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Abstract

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.

Keywords

Finite element methodMagnetohydrodynamics.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 3 , May 2002 , pp. 517 - 536
Copyright
© EDP Sciences, SMAI, 2002

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