Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. firstname.lastname@example.org.
2 Department of Mathematical Sciences, University of Alberta Edmonton, Alberta, Canada T6G 2G1, Canada. email@example.com.
Revised: 3 March 2002
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.
Mathematics Subject Classification: 65N35 / 65N25 / 65F05 / 35J05
Key words: Finite element method / Magnetohydrodynamics.
© EDP Sciences, SMAI, 2002