The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem

Energy error estimates for a linear scheme to approximate nonlinear parabolic problems

“…The results II.l and IL2 above extend and improve the ones known for other linearized schemes (see [8,31,16,10,12,27] and the références given therein), and they are obtained under minimal regularity of the data occurring in (1.1) (see section 4.2). Our scheme is in the spirit of the Laplace-modified forward Galerkin method of Douglas & Dupont [9] for non-degenerate problems and of the alternating-phase truncation method of Rogers, Berger & Ciment [25] for degenerate problems.…”

Curvature and solidification

“…derived from the Gibbs-Thomson relation, involve the boundary's curvature (see e.g .• Turnbull [22], Sekerka [15]; Langer [7], Smith [20]). The method of solution relies on a weak "enthalpy" formulation, previously studied for simpler problems by Rogers et al [14], Shamsundar and Sparrow [19], Brezis and Crandall [1], Majda [8]. The enthalpy formulation has already been adapted to the present problem, along different lines.…”

“…A temperature field is given at t = O. At points interior to either I or W the evolution of the temperature is described by the heat equation; for the sake of simplicity we assume the thermal diffusivities of both "ice" and "water" are equal to 1 (the case of phases With non-equal diffusivities can be readily handled by the method of alternate phase truncation [14].) In r. …”

Influence of the Mutation Operator on the Solution of an Inverse Stefan Problem by Genetic Algorithms

“…The solution will consist in minimization of the functional whose value is the norm of the difference between the given interface position and the position reconstructed for the selected convective heat-transfer coefficient. For the minimization of the functional genetic algorithms were used, whereas the Stefan problem was solved by an alternating phase truncation method [4]. The paper presents the influence of choice of the mutation operator on the accuracy of the results obtained.…”