A hybrid formulation of eddy current problems

In this article we examine the well-known magneto-quasistatic eddy current model for the behavior of low-frequency electromagnetic fields. We restrict ourselves to formulations in the frequency domain and linear materials, but admit rather general topological arrangements. The generic eddy current model allows two dual formulations, which may be dubbed E-based and H-based. We investigate the so-called hybrid approach that combines both formulations by means of coupling conditions across the boundaries of conducting regions. The resulting continuous and discrete variational formulations will be discussed, and an optimal error estimate for edge finite elements will be proved. It is worthy to note that for this approach no difficulties arise from the topology of the conducting regions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005