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Stable phase field approximations of anisotropic solidification

URN to cite this document:
urn:nbn:de:bvb:355-epub-279047
Barrett, John W. ; Garcke, Harald ; Nürnberg, Robert
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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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