Análisis Numérico de un Problema Estacionario de Stefan a dos Fases con Energía Interna

Abstract

We study the problem of the steady temperature distribution of a body or a container wtth a fluid, which is
submited to an internal energy g.
We assume the body to be a bounded polygonal domain ΩCRn, with a sufficiently regular boundary Г=Г1 U Г2 U Г3 and Г2 being disjoint portions of ӘΩ of positive (n-l) dimensional measure. Assuming a phase-change temperature of 0ºC for the material occupying Ω we maintain a heat flux q on Г2, a null heat flux
on Г3 and keep Г1 at the temperature (θ=b > O. In that case Garguichevich and Tarzia proved that a phase change
takes place in Ω if the internal energy g in Ω and the outflow of heat q through Г2 are small and large enough
respectively.
In the present work we follow the ideas developed in D.A.Tarzia, "Numerical Analysis for the Heat Flux in a
Mixed Elliptic Problem to obtain a Discrete Steady - State Two - Phase Stefan Problems, Rapport de Recherche
INRIA Nº1593, Rocquencourt (1992) for the case g = 0 in Ω. We consider a regular triangulation of the domain Ω
with Lagrange triangles of type 1 and we study sufficient (and/or necessary) conditions for the data to obtain a
change of phase into the corresponding discretized domain, that is a discrete temperature of non-constant sign.