Stability of flat interfaces during semidiscrete solidification

Andreas Veeser

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 4, page 573-595
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Veeser, Andreas. "Stability of flat interfaces during semidiscrete solidification." ESAIM: Mathematical Modelling and Numerical Analysis 36.4 (2010): 573-595. <http://eudml.org/doc/194117>.

@article{Veeser2010,
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. },
author = {Veeser, Andreas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {(Mullins-Sekerka) stability analysis; morphological instabilities; spatial semidiscretization; moving finite elements; phase transitions; surface tension; Stefan condition; dendritic growth; secondary sidebranching.; Mullins-Sekerka stability analysis; spatial semidiscretization; phase transitions; secondary sidebranching},
language = {eng},
month = {3},
number = {4},
pages = {573-595},
publisher = {EDP Sciences},
title = {Stability of flat interfaces during semidiscrete solidification},
url = {http://eudml.org/doc/194117},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Veeser, Andreas
TI - Stability of flat interfaces during semidiscrete solidification
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 573
EP - 595
AB - 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.
LA - eng
KW - (Mullins-Sekerka) stability analysis; morphological instabilities; spatial semidiscretization; moving finite elements; phase transitions; surface tension; Stefan condition; dendritic growth; secondary sidebranching.; Mullins-Sekerka stability analysis; spatial semidiscretization; phase transitions; secondary sidebranching
UR - http://eudml.org/doc/194117
ER -

References

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