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. © 2010 Elsevier Inc.
On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 229:18(2010), pp. 6270-6299. [10.1016/j.jcp.2010.04.039]
On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth
Nürnberg R.
2010-01-01
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 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. © 2010 Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
