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.
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This work has been supported by the Austrian Science Fund “Fonds zur Förderung der wissenschaftlichen Forschung (FWF)” under the grants SFB F013, P 14953 and START Y192.
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Bachinger, F., Langer, U. & Schöberl, J. Numerical analysis of nonlinear multiharmonic eddy current problems. Numer. Math. 100, 593–616 (2005). https://doi.org/10.1007/s00211-005-0597-2
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DOI: https://doi.org/10.1007/s00211-005-0597-2