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Algorithms 2009, 2(3), 1177-1220; doi:10.3390/a2031177

Stefan Problem through Extended Finite Elements: Review and Further Investigations

1,*  and 2
1 DICeA, Università di Firenze, via di Santa Marta 3, I-50139 Firenze, Italy 2 School of Engineering Sciences, University of Southampton, Highfield, SO171BJ Southampton, UK
* Author to whom correspondence should be addressed.
Received: 2 August 2009 / Revised: 16 September 2009 / Accepted: 17 September 2009 / Published: 21 September 2009
(This article belongs to the Special Issue Numerical Simulation of Discontinuities in Mechanics)


A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments for the blending elements. An embeddeddiscontinuity finite element approach is also developed and compared with the extended finite element method, so that a clearer insight of the latter can be given. Numerical examples for melting/solidification in planar, cylindrical, and spherical symmetry are presented and the results are compared with analytical solutions.
Keywords: first-order phase transition; extended finite elements; embedded discontinuities first-order phase transition; extended finite elements; embedded discontinuities
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Salvatori, L.; Tosi, N. Stefan Problem through Extended Finite Elements: Review and Further Investigations. Algorithms 2009, 2, 1177-1220.

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