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Finite element Galerkin methods for multi-phase Stefan problems. (English) Zbl 0533.65080

Aus physikalischen Erhaltungssätzen werden für Mehrphasen-Stefan- Probleme integrale Formulierungen hergeleitet. Mit Galerkin- und Finite Element-Ansätzen in einer und zwei Raumdimensionen werden sodann numerische Näherungsverfahren aufgestellt. Diese simulieren sowohl die physikalischen Erhaltunseigenschaften und tragen auch komplizierteren Geometrien Rechnung. Eine der Methoden widmet sich besonders der möglichst genauen Berechnung des freien Randes und gleichzeitig der Temperatur in dessen Nähe. Durch eine Reihe von Beispielen werden diese interessanten Untersuchungen veranschaulicht. Die Verfahren eignen sich gut zur Verwendung von Standard-Programmen.
Reviewer: F.v.Finckenstein

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80A17 Thermodynamics of continua
35K05 Heat equation
35R35 Free boundary problems for PDEs
35R30 Inverse problems for PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
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References:

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