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heat equation; Stefan problem; phase change; Rothe method; moving boundary value problem; imperfect contact; solidification of steel; numerical example
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.
[b9] J. L. Desbiolles, J. J. Droux, J. Rapaz, M. Rapaz: Simulation of solidification of alloys by the finite element method. An advanced course on the Finite Element Methods in Physics, European Association of Physics, Lausanne (Switzerland), 1987.
[b4] A. Handlovičová: Errors estimates of a linear approximation schemes for nonlinear difussion problems. Acta Math. Univ. Comenianae LXI, 1 (1992), 27–39.
[b1] W. Jäger, J. Kačur: Solution of porous medium type systems by linear approximation schemes. Preprint 540, Universität Heidelberg SFB 1233, 1989. MR 1137200
[b3] J. Kačur, A. Handlovičová, M. Kačurová: Solution of nonlinear diffusion problems by linear approximation schemes. SIAM Num. Anal. 30 (1993), 1703–1722. DOI 10.1137/0730087 | MR 1249039
[b31] J. Kačur, S. Luckhaus: Approximation of degenerate parabolic systems by nondegenerate elliptic parabolic systems. Preprint M2-91, Comenius University, Bratislava. MR 1609151
[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. MR 0863161 | Zbl 0593.35094
[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
[b6] R. H. Nochetto, C. Verdi: Approximation of degenerate parabolic problems using numerical integration. SIAM J. numer. anal. 35 (1988), no. 4, 784–814. DOI 10.1137/0725046 | MR 0954786
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