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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.
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.
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