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Finite Elements for the Time Harmonic Maxwell’s Equations

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Computational Electromagnetics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 28))

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Summary

We review the time harmonic Maxwell’s system and its approximation via the finite element method. The problem under consideration is strictly related to the so-called interior Maxwell’s eigenproblem.

Standard nodal (Lagrangian) elements are known to provide useless results on general meshes. Special two-dimensional meshes have been shown to give good results, but the use of them is not recommended. The use of a penalty strategy with nodal elements has been proved to give wrong results for domains with singularities. Some special schemes, which make use of nodal elements, circumvent this problem; one of them is described in this paper.

On the other hand the so-called edge elements represent the natural choice. A new proof of convergence for a method based on edge elements is summarized.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100, Pavia, Italy

    Daniele Boffi

Authors
  1. Daniele Boffi
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19717, USA

    Peter Monk

  2. Institute for Applied Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Carsten Carstensen

  3. Institute of Mathematics, University of Erlangen-Nürnberg, Bismarckstraße 1 1/2, 91054, Erlangen, Germany

    Stefan Funken

  4. Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Liepzig, Germany

    Wolfgang Hackbusch

  5. Department of Mathematics, University of Augsburg, Universitätsstraße 14, 86159, Augsburg, Germany

    Ronald H. W. Hoppe

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© 2003 Springer-Verlag Berlin Heidelberg

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Boffi, D. (2003). Finite Elements for the Time Harmonic Maxwell’s Equations. In: Monk, P., Carstensen, C., Funken, S., Hackbusch, W., Hoppe, R.H.W. (eds) Computational Electromagnetics. Lecture Notes in Computational Science and Engineering, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55745-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-55745-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44392-6

  • Online ISBN: 978-3-642-55745-3

  • eBook Packages: Springer Book Archive

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