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 Cet article a éte moissonné depuis la source 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. 
@article{RLIN_1997_9_8_4_a3,
     author = {Nochetto, Ricardo H. and Schmidt, Alfred and Verdi, Claudio},
     title = {Adapting meshes and time-steps for phase change problems},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {273--292},
     year = {1997},
     volume = {Ser. 9, 8},
     number = {4},
     zbl = {0910.65106},
     mrnumber = {MR1631617},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1997_9_8_4_a3/}
}
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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/