Stability of flat interfaces during semidiscrete solidification
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, p. 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 : https://doi.org/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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
pages = {573-595},
doi = {10.1051/m2an:2002026},
zbl = {1137.65404},
mrnumber = {1932305},
language = {en},
url = {http://www.numdam.org/item/M2AN_2002__36_4_573_0}
}

Veeser, Andreas. Stability of flat interfaces during semidiscrete solidification. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, pp. 573-595. doi : 10.1051/m2an:2002026. http://www.numdam.org/item/M2AN_2002__36_4_573_0/

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