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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.Date of publication of this fulltext: 13 Mar 2013 09:54
Monograph
DOI to cite this document: 10.5283/epub.27904
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
Involved Institutions
Details
| Item type | Monograph (Working Paper) | ||||||||||
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Volume: | 19/2012 | ||||||||||
| Date | 2012 | ||||||||||
| Institutions | Mathematics > Prof. Dr. Harald Garcke | ||||||||||
| Classification |
| ||||||||||
| 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 | ||||||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-279047 | ||||||||||
| Item ID | 27904 |
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