{"id":"https://openalex.org/W2064272241","doi":"https://doi.org/10.3390/a2031177","title":"Stefan Problem through Extended Finite Elements: Review and Further Investigations","display_name":"Stefan Problem through Extended Finite Elements: Review and Further Investigations","publication_year":2009,"publication_date":"2009-09-21","ids":{"openalex":"https://openalex.org/W2064272241","doi":"https://doi.org/10.3390/a2031177","mag":"2064272241"},"language":"en","primary_location":{"id":"doi:10.3390/a2031177","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031177","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1177/pdf?version=1253506832","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/2/3/1177/pdf?version=1253506832","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024491073","display_name":"Luca Salvatori","orcid":"https://orcid.org/0000-0002-2192-0258"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["GB","IT"],"is_corresponding":true,"raw_author_name":"Luca Salvatori","raw_affiliation_strings":["DICeA, Universit\u00e0 di Firenze, via di Santa Marta 3, I-50139 Firenze, Italy","University of Southampton"],"affiliations":[{"raw_affiliation_string":"DICeA, Universit\u00e0 di Firenze, via di Santa Marta 3, I-50139 Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Southampton","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045174791","display_name":"Niccol\u00f2 Tosi","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Niccol\u00f2 Tosi","raw_affiliation_strings":["School of Engineering Sciences, University of Southampton, Highfield, SO171BJ Southampton, UK","university of Florence"],"affiliations":[{"raw_affiliation_string":"School of Engineering Sciences, University of Southampton, Highfield, SO171BJ Southampton, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"university of Florence","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024491073"],"corresponding_institution_ids":["https://openalex.org/I43439940","https://openalex.org/I45084792"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":8.8113,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.97895687,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"3","first_page":"1177","last_page":"1220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10717","display_name":"Aluminum Alloys Composites Properties","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.8697519898414612},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5932945013046265},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5201550126075745},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5071988105773926},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.44640302658081055},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4385876953601837},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43423566222190857},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3979000449180603},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34501779079437256},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33695656061172485},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25255703926086426},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23571380972862244},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08525925874710083}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8697519898414612},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5932945013046265},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5201550126075745},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5071988105773926},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.44640302658081055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4385876953601837},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43423566222190857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3979000449180603},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34501779079437256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33695656061172485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25255703926086426},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23571380972862244},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08525925874710083},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a2031177","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031177","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1177/pdf?version=1253506832","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/365028","is_oa":true,"landing_page_url":"http://hdl.handle.net/2158/365028","pdf_url":"http://www.mdpi.com/1999-4893/2/3/1177","source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e03265916303424b85339fe8b3101879","is_oa":true,"landing_page_url":"https://doaj.org/article/e03265916303424b85339fe8b3101879","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 2, Iss 3, Pp 1177-1220 (2009)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a2031177","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031177","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1177/pdf?version=1253506832","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2064272241.pdf","grobid_xml":"https://content.openalex.org/works/W2064272241.grobid-xml"},"referenced_works_count":71,"referenced_works":["https://openalex.org/W234828779","https://openalex.org/W417564618","https://openalex.org/W1589288858","https://openalex.org/W1591608973","https://openalex.org/W1963942672","https://openalex.org/W1970833450","https://openalex.org/W1972481426","https://openalex.org/W1972842770","https://openalex.org/W1973067660","https://openalex.org/W1974288061","https://openalex.org/W1980099947","https://openalex.org/W1980950607","https://openalex.org/W1985415913","https://openalex.org/W1998428203","https://openalex.org/W1998745245","https://openalex.org/W2001194406","https://openalex.org/W2010345849","https://openalex.org/W2011835464","https://openalex.org/W2014073700","https://openalex.org/W2018039791","https://openalex.org/W2019341779","https://openalex.org/W2020005049","https://openalex.org/W2021150939","https://openalex.org/W2024688047","https://openalex.org/W2026742541","https://openalex.org/W2028691187","https://openalex.org/W2030604754","https://openalex.org/W2040595976","https://openalex.org/W2042900525","https://openalex.org/W2046978152","https://openalex.org/W2056528953","https://openalex.org/W2066202211","https://openalex.org/W2070087425","https://openalex.org/W2070407007","https://openalex.org/W2070663975","https://openalex.org/W2071181124","https://openalex.org/W2078644288","https://openalex.org/W2081784455","https://openalex.org/W2083662733","https://openalex.org/W2090657659","https://openalex.org/W2091772847","https://openalex.org/W2092011174","https://openalex.org/W2092147349","https://openalex.org/W2093834886","https://openalex.org/W2098186902","https://openalex.org/W2098258814","https://openalex.org/W2109643463","https://openalex.org/W2109911863","https://openalex.org/W2115594660","https://openalex.org/W2127693549","https://openalex.org/W2130011046","https://openalex.org/W2137198182","https://openalex.org/W2139933850","https://openalex.org/W2140219336","https://openalex.org/W2147384385","https://openalex.org/W2148619027","https://openalex.org/W2150801324","https://openalex.org/W2151793763","https://openalex.org/W2157721313","https://openalex.org/W2158189438","https://openalex.org/W2161005552","https://openalex.org/W2161933996","https://openalex.org/W2162683419","https://openalex.org/W2167200576","https://openalex.org/W2281167255","https://openalex.org/W2564164372","https://openalex.org/W2774580773","https://openalex.org/W2989643232","https://openalex.org/W4247020594","https://openalex.org/W6695346545","https://openalex.org/W6790340191"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2010821947","https://openalex.org/W4234008889","https://openalex.org/W1573186872","https://openalex.org/W2071722255","https://openalex.org/W2165887158","https://openalex.org/W2352023866","https://openalex.org/W2021654023","https://openalex.org/W2350569191"],"abstract_inverted_index":{"A":[0],"general":[1],"review":[2],"of":[3,15,77],"the":[4,13,30,45,53,67,78,96],"extended":[5,68],"finite":[6,58,69],"element":[7,59,70],"method":[8],"and":[9,33,37,48,64,90,95],"its":[10],"application":[11],"to":[12],"simulation":[14],"first-order":[16],"phase":[17],"transitions":[18],"is":[19,61],"provided.":[20],"Detailed":[21],"numerical":[22,42],"investigations":[23],"are":[24,93,98],"then":[25],"performed":[26],"by":[27],"focusing":[28],"on":[29],"one-dimensional":[31],"case":[32],"studying:":[34],"(i)":[35],"spatial":[36],"temporal":[38],"discretisations,":[39],"(ii)":[40],"different":[41,50],"techniques":[43],"for":[44,52,85],"interface-condition":[46],"enforcement,":[47],"(iii)":[49],"treatments":[51],"blending":[54],"elements.":[55],"An":[56],"embeddeddiscontinuity":[57],"approach":[60],"also":[62],"developed":[63],"compared":[65,99],"with":[66,100],"method,":[71],"so":[72],"that":[73],"a":[74],"clearer":[75],"insight":[76],"latter":[79],"can":[80],"be":[81],"given.":[82],"Numerical":[83],"examples":[84],"melting/solidification":[86],"in":[87],"planar,":[88],"cylindrical,":[89],"spherical":[91],"symmetry":[92],"presented":[94],"results":[97],"analytical":[101],"solutions.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
