The Time-Harmonic Eddy-Current Problem in General Domains: Solvability via Scalar Potentials

  • Ana Alonso Rodríguez
  • Paolo Fernandes
  • Alberto Valli
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 28)


The eddy-current problem for the time-harmonic Maxwell equations in domains of general topology is solved by introducing a scalar “potential” for the magnetic field in the insulator part of the domain. Indeed, since in general the insulator Ω I is multiply-connected, the magnetic field differs from the gradient of a potential by a harmonic field. We rewrite the problem in a two-domain formulation, in term of a scalar magnetic potential and a harmonic field in Ω I . Then the finite element numerical approximation based on this two-domain formulation is presented, using edge elements in the conductor and nodal elements in the insulator, and an optimal error estimate is proved. An iteration-by-sub domain procedure for the solution of the problem is also proposed.


General Domain Duality Pairing Mixed Finite Element Finite Element Space Optimal Error Estimate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ana Alonso Rodríguez
    • 1
  • Paolo Fernandes
    • 2
  • Alberto Valli
    • 3
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  2. 2.Istituto per la Matematica Applicata del C.N.R.GenovaItaly
  3. 3.Dipartimento di MatematicaUniversità di TrentoPovo (Trento)Italy

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