In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward integral formulation Stefan problem when parameter approaches zero. Assuming natural physical assumption that initial condition constrained, but taking more general boundary conditions, prove solution relaxed converges a stronger way to classical weak problem.

We consider in this paper the time-dependent two-phase Stefan problem and derive a posteriori error estimates and adaptive strategies for its conforming spatial and backward Euler temporal discretizations. Regularization of the enthalpy–temperature function and iterative linearization of the arising systems of nonlinear algebraic equations are considered. Our estimators yield a guaranteed and f...

1. Introduction The classical Stefan problem is a model for phase transitions in solid-liquid systems and accounts for heat diiusion and exchange of latent heat in a homogeneous medium. The strong formulation of this model corresponds to a moving boundary problem involving a parabolic diiusion equation for each phase and a transmission condition prescribed at the interface separating the phases...

Considering the one-phase Stefan problem, we present an account of some recent mathematical results within the framework of variational inequalities. We discuss several situations corresponding to different boundary conditions and different geometries, like the exterior problem, the continuous casting model, and the degenerate case of the quasi-steady model. We develop a few continuous-dependen...

We prove that classical C 1-solutions to phase transition problems, which include the two-phase Stefan problem, are smooth. The problem is reduced to a xed domain using von Mises variables. The estimates are obtained by frozen coeecients and new L p estimates for linear parabolic equations with dynamic boundary condition. Crucial ingredients are the observation that a certain function is a Four...

In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of som...