Mixed finite element approximation of eddy current problems

Finite element approximation of eddy current problems that are entirely based on the magnetic field ${\bf H}$ are haunted by the need to enforce the algebraic constraint $\hbox{curl} {\bf H} = {\bf 0}$ in non-conducting regions. As an alternative to techniques employing combinatorial Seifert (cutting) surfaces, in order to introduce a scalar magnetic potential we propose mixed multi-field formulations, which enforce the constraint in the variational formulation. In light of the fact that the computation of cutting surfaces is expensive, the mixed finite element approximation is a viable option despite the increased number of unknowns.