Geodesic
Adapting meshes and time-steps for phase change problems
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 4, pp. 273-292.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.
Si considera l'approssimazione numerica del problema di Stefan bifase e si discute un metodo adattativo di elementi finiti basato su stime dell'errore a posteriori rigorose e su tecniche di raffinamento/deraffinamento della reticolazione. Si dimostra che il metodo è stabile e convergente sotto opportune restrizioni dell'operazione di deraffinamento e si illustra l'implementazione dell'algoritmo adattativo con un metodo di bisezione. Si conclude, infine, con alcune simulazioni di un problema che presenta una singolarità di tipo angolo, per catturare la quale è essenziale l'uso di metodi di raffinamento locale. 
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Nochetto, Ricardo H.; Schmidt, Alfred; Verdi, Claudio. Adapting meshes and time-steps for phase change problems. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 4, pp. 273-292. http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_4_a3/

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