Geodesic
Stability of flat interfaces during semidiscrete solidification
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 573-595 Cet article a éte moissonné depuis la source Numdam

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The stability of flat interfaces with respect to a spatial semidiscretization of a solidification model is analyzed. The considered model is the quasi-static approximation of the Stefan problem with dynamical Gibbs-Thomson law. The stability analysis bases on an argument developed by Mullins and Sekerka for the undiscretized case. The obtained stability properties differ from those with respect to the quasi-static model for certain parameter values and relatively coarse meshes. Moreover, consequences on discretization issues are discussed.

DOI : 10.1051/m2an:2002026
Classification : 65M12, 65M60
Keywords: (Mullins-Sekerka) stability analysis, morphological instabilities, spatial semidiscretization, moving finite elements, phase transitions, surface tension, Stefan condition, dendritic growth, secondary sidebranching 
@article{M2AN_2002__36_4_573_0,
     author = {Veeser, Andreas},
     title = {Stability of flat interfaces during semidiscrete solidification},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {573--595},
     year = {2002},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     doi = {10.1051/m2an:2002026},
     mrnumber = {1932305},
     zbl = {1137.65404},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002026/}
}
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Veeser, Andreas. Stability of flat interfaces during semidiscrete solidification. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 573-595. doi: 10.1051/m2an:2002026

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