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.
Caloric measure and Reifenberg flatness.
Computation of bifurcated branches in a free boundary problem arising in combustion theory
Computation of bifurcated branches in a free boundary problem arising in combustion theory
We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter does not exceed a critical value . The latter is the limit of a decreasing sequence of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...
Computational studies of anisotropic diffuse interface model of microstructure formation in solidification
Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions.
Convergence to equilibria for a three-dimensional conserved phase-field system with memory.
Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys.
Correctors and error estimates in the homogenization of a Mullins–Sekerka problem
Coupled heat transport and Darcian water flow in freezing soils
The model of coupled heat transport and Darcian water flow in unsaturated soils and in conditions of freezing and thawing is analyzed. In this contribution, we present results concerning the existence of the numerical solution. Numerical scheme is based on semi-implicit discretization in time. This work illustrates its performance for a problem of freezing processes in vertical soil columns.
Co-volume methods for degenerate parabolic problems.