Numerische Mathematik

, Volume 100, Issue 4, pp 593–616 | Cite as

Numerical analysis of nonlinear multiharmonic eddy current problems

Article

Summary

This work is devoted to non-linear eddy current problems and their numerical treatment by the so-called multiharmonic approach. Since the sources are usually alternating currents, we propose a truncated Fourier series expansion instead of a costly time-stepping scheme. Moreover, we suggest to introduce some regularization parameter that ensures unique solvability not only in the factor space of divergence-free functions, but also in the whole space H(curl). Finally, we provide a rigorous estimate for the total error that is due to the use of truncated Fourier series, the regularization technique and the spatial finite element discretization.

Mathematics Subject Classification (2001)

65M60 65T40 78M10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Spezialforschungsbereich SFB F013 “Numerical and Symbolic Scientific Computing”Johannes Kepler University LinzAustria
  2. 2.Institute for Computational MathematicsJohannes Kepler University LinzAustria
  3. 3.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesAustria

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