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

Stefan Problem through Extended Finite Elements: Review and Further Investigations

DICeA, Università di Firenze, via di Santa Marta 3, I-50139 Firenze, Italy
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 3.0).

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MDPI and ACS Style

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

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