, Volume 22, Issue 3, pp 351-381

On the numerical approach to a two-phase stefan problem with non-linear flux

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Abstract

This paper is devoted to the numerical analysis of a multidimensional two-phase Stefan problem, with a non-linear flux condition on the fixed boundary; the enthalpy formulation is used. A numerical approach suggested by the theory of non-linear semigroup of contractions in L1 (Ω) is introduced; some converging algorithms based on the Crandall-Liggett formula and on the non-linear Chernoff formula are studied. The algebraic non-linear equations are solved by a modified Gauss-Seidel method. The results of several numerical tests are exhibited and discussed.

This work was supported by Ministero Pubblica Istruzione (fondi per la ricerca scientifica) and by Istituto di Analisi Numerica del C.N.R., Pavia.