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.

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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