Mixed finite element approximation of eddy current problems

Finite element approximations of eddy current problems that are entirely based on the magnetic field H are haunted by the need to enforce the algebraic constraint curl H=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.