A class of time discrete schemes for a phase-field system of Penrose-Fife type
A class of time discrete schemes for a phase–field system of Penrose–Fife type
In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.
A diffused interface whose chemical potential lies in a Sobolev space
We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms of the associated chemical potential fields are bounded uniformly, where and is the dimension of the domain. We show that the limit interface as tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.
A domain splitting method for heat conduction problems in composite materials
A domain splitting method for heat conduction problems in composite materials
We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of fibres embedded into some standard material. For ease of presentation we consider the case of two space dimensions only. The set of finite element equations obtained by the backward Euler scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually enhanced...
A generalized solution to a Cahn-Hilliard/Allen-Cahn system.
A numerical scheme for the two phase Mullins-Sekerka problem.
A one-dimensional spot welding model.
A parallel algorithm for two phase multicomponent contaminant transport
We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...
A semidiscretization scheme for a phase-field type model for solidification.
A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...
A stationary Stefan problem with convection and nonlinear diffusion.
About mathematical models of phase transitions.
An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems
This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and make it possible...
An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
Using the approach in [5] for analysing time discretization error and assuming more regularity on the initial data, we improve on the error bound derived in [2] for a fully practical piecewise linear finite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy with non-smooth free energy.
Analyse mathématique des transferts thermiques dans des systèmes dispersés subissant des transformations de phases
Analysis of equations in the phase-field model
Analysis of the mushy region in conduction-convection problems with change of phase.
Analytic solution of an initial-value problem from Stokes flow with free boundary.