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Title: The use of linear approximation scheme for solving the Stefan problem (English)
Author: Dzurenda, Peter
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 42
Issue: 1
Year: 1997
Pages: 35-56
Summary lang: English
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Category: math
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Summary: This paper deals with the linear approximation scheme to approximate a singular parabolic problem: the two-phase Stefan problem on a domain consisting of two components with imperfect contact. The results of some numerical experiments and comparisons are presented. The method was used to determine the temperature of steel in the process of continuous casting. (English)
Keyword: heat equation
Keyword: Stefan problem
Keyword: phase change
Keyword: Rothe method
Keyword: moving boundary value problem
Keyword: imperfect contact
Keyword: solidification of steel
Keyword: numerical example
MSC: 35K05
MSC: 35R35
MSC: 65M20
MSC: 65M30
MSC: 65N30
MSC: 65Z05
MSC: 80A20
MSC: 80A22
idZBL: Zbl 0902.65072
idMR: MR1426679
DOI: 10.1023/A:1022240626467
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Date available: 2009-09-22T17:53:24Z
Last updated: 2015-05-20
Stable URL: http://hdl.handle.net/10338.dmlcz/134343
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Reference: [b31] J. Kačur, S. Luckhaus: Approximation of degenerate parabolic systems by nondegenerate elliptic parabolic systems.Preprint M2-91, Comenius University, Bratislava. MR 1609151
Reference: [b24] R. H. Nochetto: Error estimates for multidimensional Stefan problems with general boundary conditions.Research Notes in Math. 120, Pitman, Boston, 1985, pp. 50–60. Zbl 0593.35094, MR 0863161
Reference: [b7] R. H. Nochetto, C. Verdi: An efficent linear scheme to approximate parabolic free boundary problems: error estimates and implementation.American Math. Society, 1988, pp. 27–53. MR 0942142
Reference: [b6] R. H. Nochetto, C. Verdi: Approximation of degenerate parabolic problems using numerical integration.SIAM J. numer. anal. 35 (1988), no. 4, 784–814. MR 0954786, 10.1137/0725046
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