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On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth

Barrett, John W. and Garcke, Harald and Nürnberg, Robert (2010) On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. J. Comput. Phys. 229, pp. 6270-6299.

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Abstract

We introduce a parametric finite element approximation for the Stefan problem with the Gibbs–Thomson law and kinetic undercooling, which mimics the underlying energy structure of the problem. The proposed method is also applicable to certain quasi-stationary variants, such as the Mullins–Sekerka problem. In addition, fully anisotropic energies are easily handled. The approximation has ...

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Item Type:Article
Date:2010
Institutions:Mathematics > Prof. Dr. Harald Garcke
Classification:
NotationType
35K55MSC
35R35MSC
53C44MSC
65M12MSC
65M50MSC
65M60MSC
74E10MSC
74E15MSC
80A22MSC
82C26MSC
UNSPECIFIEDMSC
UNSPECIFIEDMSC
Keywords:Stefan problem, Mullins–Sekerka problem, surface tension, anisotropy, kinetic undercooling, Gibbs–Thomson law, dendritic growth, snow crystal growth; parametric finite elements
Subjects:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Partially
Owner: Eva Ruetz
Deposited On:23 Mar 2010 08:15
Last Modified:13 Mar 2014 13:08
Item ID:13662
Owner Only: item control page
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