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To the Numerical Solution of an Inverse Stefan Problem in Two Space Variables

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Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben

Abstract

The application of Gauss-Newton’s procedure to the inverse Stefan problem requires the computation of the Fréchét derivative of the solution operator S: g ↦ s assigning to each control g the corresponding free boundary s. Analogously to the one-dimensional case the defining formulas are developed as a necessary condition for Fréchét differentiability in a simple two-dimensional one-phase problem.

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References

  1. Friedman, A. and Kinderlehrer, D.: A One Phase Stefan Problem. Ind. Univ. Math. J. 24 (1975), 1005–1035

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität München, Theresienstr. 39 b, D-8000, München 2, Germany

    Dr. Peter Jochum

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  1. Dr. Peter Jochum
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, D-3392, Clausthal-Zellerfeld, Germany

    J. Albrecht

  2. Institut für Angewandte Mathematik, Universität Hamburg, Bundesstrasse 55, D-2 Hamburg 13, Germany

    L. Collatz

  3. Institut für Mathematik III, Freie Universität Berlin, Arnimallee 2-6, D-1 Berlin 33, Germany

    K.-H. Hoffmann

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© 1982 Springer Basel AG

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Jochum, P. (1982). To the Numerical Solution of an Inverse Stefan Problem in Two Space Variables. In: Albrecht, J., Collatz, L., Hoffmann, KH. (eds) Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6563-0_9

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  • DOI: https://doi.org/10.1007/978-3-0348-6563-0_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6565-4

  • Online ISBN: 978-3-0348-6563-0

  • eBook Packages: Springer Book Archive

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