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Stable phase field approximations of anisotropic solidification

Barrett, John W., Garcke, Harald and Nürnberg, Robert (2012) Stable phase field approximations of anisotropic solidification. Preprintreihe der Fakultät Mathematik 19/2012, Working Paper.

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Date of publication of this fulltext: 13 Mar 2013 09:54

Abstract

We introduce unconditionally stable finite element approximations for a phase
field model for solidification, which take highly anisotropic surface energy and kinetic
effects into account. We hence approximate Stefan problems with anisotropic
Gibbs{Thomson law with kinetic undercooling, and quasi-static variants thereof.
The phase field model is given by
#wt + � %(') 't = r: (b(')rw) ;
c
a
� %(')w = " �
� �(r') 't


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Item type:Monograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Date:2012
Institutions:Mathematics > Prof. Dr. Harald Garcke
Classification:
NotationType
65M60MSC
65M12MSC
35K55MSC
74N20MSC
Keywords:phase field models, parabolic partial differential equations, Stefan problem, anisotropy, Allen{Cahn equation, viscous Cahn{Hilliard equation, crystal growth, finite element approximation
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Unknown
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Item ID:27904
Owner only: item control page

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