Analytic solutions for the classical two-phase Stefan problem
Application of the multigrid methods for solving Stefan problem
Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation
Approximation of a solidification problem
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri,...
Approximation of crystalline dendrite growth in two space dimensions.
Approximation of parabolic equations using the Wasserstein metric
Approximation of Parabolic Equations Using the Wasserstein Metric
We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the variational...
Asymptotic analysis to a phase-field model with a nonsmooth memory kernel.
Asymptotic behaviour of the interface for the critical case of undercooled Stefan problem
The critical case of solvability of a two-phase Stefan problem with supercooled liquid phase is considered. Asymptotic analysis is performed of the behaviour of the free boundary in the vicinity of the initial time.
Asymptotic justification of the conserved phase-field model with memory.