Abstract
A survey of results of a finite element procedure based on the idea of straightening the moving boundary is given together with additional remarks concerning the numerical computations.
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Literatur
Douglas, J., Jr., T. Dupont and M. F. Wheeler (1974): H1-Galerkin methods for the Laplace and heat equations. Math. Aspects of Finite Elements in Part. Diff. Equs., C. de Boor ed., Academic Press, 383–416.
Helfrich, H.P. (1974): Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen. Manuscripta Math. 15, 219–235.
Magenes, E. (1976): Topics in parabolic equations: some typical free boundary problems. Boundary value problems for linear partial differential equations, Proceedings of the NATO Advanced Study Institute held at Liège, Belgium, Sept. 6–17, 1976; H.G. Garnier ed., D. Reidel Publ. Comp. Dortrecht, 239–312.
Nitsche, J.A. (α) (1978): Finite element approximation to the one-dimensional Stefan problem. Proceedings on Recent Advance in Numerical Analysis, C. de Boor and G. Golub eds., Academic Press, 119–142.
Nitsche, J.A. (β) (1980): Approximation des eindimensionalen Stefan-Problems durch finite Elemente. International Congress of Mathematicians, Helsinki, Aug. 15–23, 1978; O. Lehto ed., Acad. Sci. Fennica, 923–928.
Nitsche, J.A. (γ) (1960): Finite element approximations for free boundary problems. TICOM Second International Conference on Computational Methods in Nonlinear Mechanics, Austin, Mar. 26–29, 1979; Comp. Methods in Nonlinear Mechanics, J.T. Oden ed., North Holland Publ. Co., 341–360.
Nitsche, J.A. (δ) (1980): A finite element method for parabolic free boundary problems. Free Boundary Problems, Proceedings of a seminar held in Pavia, Sept.-Oct. 1979, E. Magenes ed., 277–318.
Sammon, P.H. (1978): Approximations for parabolic equations with time dependent coefficients. Cornell University.
Stefan, J. (1669): Über einige Probleme der Theorie der Wärmeleitung. Sitz.-Ber. Wien Akad. Math. Naturw. 96, 473–484.
Stoer, J., R. Bulirsch (1978): Einführung in die Numerische Mathematik II, 2. Auflage, Springer-Verlag, Berlin.
Thomée, V. (1974): Some convergence results for Galerkin methods for parabolic boundary value problems. Math. Aspects of Finite Elements in Part. Diff. Equs., C. de Boor ed., Academic Press, 55–88.
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© 1982 Springer Basel AG
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Nitsche, J. (1982). Moving Boundary Problems and Finite Elements. 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_17
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DOI: https://doi.org/10.1007/978-3-0348-6563-0_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6565-4
Online ISBN: 978-3-0348-6563-0
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