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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.
@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},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
doi = {10.1051/m2an:2002026},
mrnumber = {1932305},
zbl = {1137.65404},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002026/}
}
TY - JOUR AU - Veeser, Andreas TI - Stability of flat interfaces during semidiscrete solidification JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2002 SP - 573 EP - 595 VL - 36 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002026/ DO - 10.1051/m2an:2002026 LA - en ID - M2AN_2002__36_4_573_0 ER -
%0 Journal Article %A Veeser, Andreas %T Stability of flat interfaces during semidiscrete solidification %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2002 %P 573-595 %V 36 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002026/ %R 10.1051/m2an:2002026 %G en %F M2AN_2002__36_4_573_0
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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