Barrett, John W. and Garcke, Harald and Nürnberg, Robert
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.
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 good
mesh properties, leading to a well-conditioned discretization, even in three space
dimensions. Several numerical computations, including for dendritic growth and
for snow crystal growth, are presented.
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||Stefan problem, Mullins–Sekerka problem, surface tension, anisotropy,
kinetic undercooling, Gibbs–Thomson law, dendritic growth, snow crystal growth; parametric
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Partially|
|Deposited On:||23 Mar 2010 08:15|
|Last Modified:||20 Jul 2011 22:24|