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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)

Summary

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.

Keywords

General Domain Duality Pairing Mixed Finite Element Finite Element Space Optimal Error Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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