The use of linear approximation scheme for solving the Stefan problem. (English) Zbl 0902.65072

The paper deals with a linear approximation scheme based on Rothe’s method for certain parabolic moving boundary value problems in weak formulation. In particular, the two-phase Stefan problem on a domain consisting of two components with imperfect contact is studied. As an application, a model of the heat transfer in the course of solidification of steel in the process of continuous casting with imperfect contact between the mold and the slab is discussed.
Convergence of the Rothe functions to the weak solution of the problem under consideration is proved, an iterative procedure for their construction is designed and its properties are studied. The full discretization scheme is briefly discussed as well. A numerical example documents the applicability of the method.
The paper employs and modifies the approach of J. Kačur, A. Handlovičová and M. Kačurová [SIAM J. Numer. Anal. 30, No. 6, 1703-1722 (1993; Zbl 0792.65070)] and compares the effectivity of the proposed numerical method with other similar procedures based on Rothe’s method.
Reviewer: P.Přikryl (Praha)


65Z05 Applications to the sciences
80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation


Zbl 0792.65070
Full Text: DOI EuDML


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