Anisotropic mesh adaptation for the solution of the Stefan problem

Authors:
Youssef Belhamadia;André Fortin;Éric Chamberland
Affiliations:
GIREF, Département de mathématiques et de statistique, Université Laval, Bureau 2986, Pavillon Pouliot, Qué., Canada G1K 7P4;GIREF, Département de mathématiques et de statistique, Université Laval, Bureau 2986, Pavillon Pouliot, Qué., Canada G1K 7P4;GIREF, Département de mathématiques et de statistique, Université Laval, Bureau 2986, Pavillon Pouliot, Qué., Canada G1K 7P4
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

A new finite element formulation for the solution of the classical Stefan problem is introduced. It is obtained by a slight modification of the phase-field formulation used for dendritic growth where both the phase-field φ and the temperature T are discretized. An anisotropic mesh adaptation strategy is also presented to further increase the accuracy of the method. Numerical results for two-dimensional examples illustrating the performance and accuracy of the proposed method are presented.