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Stability of flat interfaces during semidiscrete solidification

Published online by Cambridge University Press:  15 September 2002

Andreas Veeser
Andreas Veeser*
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy. veeser@mat.unimi.it. (On leave from) Institut für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg, Germany. andy@mathematik.uni-freiburg.de.
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Abstract

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.

Keywords

(Mullins-Sekerka) stability analysismorphological instabilitiesspatial semidiscretizationmoving finite elementsphase transitionssurface tensionStefan conditiondendritic growthsecondary sidebranching.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 4 , July 2002 , pp. 573 - 595
Copyright
© EDP Sciences, SMAI, 2002

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