Abstract
The aim of this article is to summarize some results which were derived in connection with the method of minimizing the defects applied to a one-dimensional degenerate Stefan problem. The method consists in approximating the unknown temperature distribution as well as the unknown phase change interface by members of linear function spaces in such a way that the arising defects become minimal. This approach leads to an approximation problem the numerical solution of which is justified by computable error bounds. The existence of a solution to the approximation problem and the global convergence of a class of algorithms for its solution can be guaranteed. A numerical example is discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cannon, J.R., Primicerio, M.: Remarks on the one-phase Stefan problem for the heat equation with flux prescribed on the fixed boundary. J. Math. Anal. Appl.35 (1971), 361–373.
Lozano, C.: An exact solution to a one phase, one dimensional Stefan problem with an emerging free boundary. Technical Report No.63A, AMI, Univ. of Delaware, 1980.
Lozano, C., Reemtsen, R.: On a Stefan problem with an emerging free boundary. Technical Report, AMI, Univ. of Delaware, 1980.
Osborne, M. R., Watson, G. A.: An algorithm for minimax approximation in the nonlinear case, The Computer J. 12 (1969), 64–69.
Reemtsen, R., Lozano, C.: An approximation technique for the numerical solution of a Stefan problem. Technical Report No. 57A, AMI, Univ. of Delaware, 1979.
Reemtsen, R.: A computer program for the numerical solution of free boundary problems. Technical Report No. 58A, AMI, Univ. of Delaware, 1979.
Reemtsen, R.: On the convergence of a class of nonlinear approximation methods. Preprint-Nr.536, TH Darmstadt, 1980.
Reemtsen, R.: On level sets and an approximation problem for the numerical solution of a free boundary problem. Preprint-Nr. 554, TH Darmstadt, 1980.
Rosenbloom, P. C., Widder, D.V.: Expansion in terms of heat polynomials and associated functions. Trans.Amer. Math. Soc. 92 (1959), 220–266.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer Basel AG
About this chapter
Cite this chapter
Reemtsen, R. (1982). The Method of Minimizing the Defects for the Stefan Problem. 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_19
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6563-0_19
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6565-4
Online ISBN: 978-3-0348-6563-0
eBook Packages: Springer Book Archive