Adapting meshes and time-steps for phase change problems
Nochetto, Ricardo H. ; Schmidt, Alfred ; Verdi, Claudio
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 8 (1997), p. 273-292 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Publié le : 1997-12-01
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     author = {Ricardo H. Nochetto and Alfred Schmidt and Claudio Verdi},
     title = {Adapting meshes and time-steps for phase change problems},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {8},
     year = {1997},
     pages = {273-292},
     zbl = {0910.65106},
     mrnumber = {1631617},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1997_9_8_4_273_0}
}

Nochetto, Ricardo H.; Schmidt, Alfred; Verdi, Claudio. Adapting meshes and time-steps for phase change problems. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 8 (1997) pp. 273-292. http://gdmltest.u-ga.fr/item/RLIN_1997_9_8_4_273_0/

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