{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:39:33Z","timestamp":1760888373015,"version":"build-2065373602"},"reference-count":65,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2009,9,21]],"date-time":"2009-09-21T00:00:00Z","timestamp":1253491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a2031177","type":"journal-article","created":{"date-parts":[[2009,9,21]],"date-time":"2009-09-21T08:23:52Z","timestamp":1253521432000},"page":"1177-1220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Stefan Problem through Extended Finite Elements: Review and Further Investigations"],"prefix":"10.3390","volume":"2","author":[{"given":"Luca","family":"Salvatori","sequence":"first","affiliation":[{"name":"DICeA, Universit\u00e0 di Firenze, via di Santa Marta 3, I-50139 Firenze, Italy"}]},{"given":"Niccol\u00f2","family":"Tosi","sequence":"additional","affiliation":[{"name":"School of Engineering Sciences, University of Southampton, Highfield, SO171BJ Southampton, UK"}]}],"member":"1968","published-online":{"date-parts":[[2009,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0022-5096(03)00091-7","article-title":"Chemically induced swelling of hydrogels","volume":"52","author":"Dolbow","year":"2004","journal-title":"Journal of the Mechanics and Physics of Solids"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4447","DOI":"10.1016\/j.cma.2004.12.004","article-title":"A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels","volume":"194","author":"Dolbow","year":"2005","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"ref_3","unstructured":"Crank, J. 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