Stability of flat interfaces during semidiscrete solidification
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 573-595.

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
Mots-clés : (Mullins-Sekerka) stability analysis, morphological instabilities, spatial semidiscretization, moving finite elements, phase transitions, surface tension, Stefan condition, dendritic growth, secondary sidebranching 
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     title = {Stability of flat interfaces during semidiscrete solidification},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {573--595},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/m2an:2002026},
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     zbl = {1137.65404},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2002026/}
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Veeser, Andreas. Stability of flat interfaces during semidiscrete solidification. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 573-595. doi : 10.1051/m2an:2002026. http://www.numdam.org/articles/10.1051/m2an:2002026/

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