On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth
作者： John W. Barrett , Harald Garcke , Robert Nürnberg
DOI: 10.1016/J.JCP.2010.04.039
关键词:
摘要: We introduce a parametric finite element approximation for the Stefan problem with Gibbs-Thomson law and kinetic undercooling, which mimics underlying energy structure of problem. The proposed method is also applicable to certain quasi-stationary variants, such as Mullins-Sekerka In addition, fully anisotropic energies are easily handled. has good mesh properties, leading well-conditioned discretization, even in three space dimensions. Several numerical computations, including dendritic growth snow crystal growth, presented.
core.ac.uk
harvard.edu
elsevier.com
sci-hub.se 参考文章(60)
Long-Qing Chen, Phase-Field Models for Microstructure Evolution Annual Review of Materials Research. ,vol. 32, pp. 113- 140 ,(2002) , 10.1146/ANNUREV.MATSCI.32.112001.132041
The phase field technique for modeling multiphase materials Reports on Progress in Physics. ,vol. 71, pp. 106501- ,(2008) , 10.1088/0034-4885/71/10/106501
JOHN W. BARRETT, CHARLES M. ELLIOTT, A Finite-element Method for Solving Elliptic Equations with Neumann Data on a Curved Boundary Using Unfitted Meshes Ima Journal of Numerical Analysis. ,vol. 4, pp. 309- 325 ,(1984) , 10.1093/IMANUM/4.3.309
Klaus Deckelnick, Gerhard Dziuk, Charles M. Elliott, Computation of geometric partial differential equations and mean curvature flow Acta Numerica. ,vol. 14, pp. 139- 232 ,(2005) , 10.1017/S0962492904000224
Kenneth G Libbrecht, The physics of snow crystals Reports on Progress in Physics. ,vol. 68, pp. 855- 895 ,(2005) , 10.1088/0034-4885/68/4/R03
Matthias Röger, Existence of Weak Solutions for the Mullins-Sekerka Flow Free Boundary Problems. ,vol. 37, pp. 361- 368 ,(2006) , 10.1007/978-3-7643-7719-9_35
Ľubomír Baňas, Robert Nürnberg, Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration Journal of Scientific Computing. ,vol. 37, pp. 202- 232 ,(2008) , 10.1007/S10915-008-9203-Y
UWE F. MAYER, A numerical scheme for moving boundary problems that are gradient flows for the area functional European Journal of Applied Mathematics. ,vol. 11, pp. 61- 80 ,(2000) , 10.1017/S0956792599003812
W. J. Boettinger, J. A. Warren, C. Beckermann, A. Karma, Phase-Field Simulation of Solidification Annual Review of Materials Research. ,vol. 32, pp. 163- 194 ,(2002) , 10.1146/ANNUREV.MATSCI.32.101901.155803
Xinfu Chen, Xinyu Deng, Peter W. Bates, A numerical scheme for the two phase Mullins-Sekerka problem. Electronic Journal of Differential Equations. ,vol. 1995, pp. 1- 27 ,(1995)