{"id":"https://openalex.org/W2038393809","doi":"https://doi.org/10.1090/s0025-5718-2014-02854-8","title":"Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem","display_name":"Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem","publication_year":2014,"publication_date":"2014-06-18","ids":{"openalex":"https://openalex.org/W2038393809","doi":"https://doi.org/10.1090/s0025-5718-2014-02854-8","mag":"2038393809"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02854-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02854-8","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02854-8/S0025-5718-2014-02854-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02854-8/S0025-5718-2014-02854-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037714004","display_name":"Daniele A. Di Pietro","orcid":"https://orcid.org/0000-0003-0959-8830"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210142014","display_name":"Institut Montpelli\u00e9rain Alexander Grothendieck","ror":"https://ror.org/044kxby82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210141950","https://openalex.org/I4210142014"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniele Di Pietro","raw_affiliation_strings":["Universit\u00c3\u00a9 Montpellier 2, I3M, 34057 Montpellier, France","Institut de Math\u00e9matiques et de Mod\u00e9lisation de Montpellier"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00c3\u00a9 Montpellier 2, I3M, 34057 Montpellier, France","institution_ids":["https://openalex.org/I19894307"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques et de Mod\u00e9lisation de Montpellier","institution_ids":["https://openalex.org/I4210142014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020083948","display_name":"Martin Vohral\u0131\u0301k","orcid":"https://orcid.org/0000-0002-8838-7689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Vohral\u00edk","raw_affiliation_strings":["Environmental Modeling, Optimization and Programming Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Environmental Modeling, Optimization and Programming Models","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090332530","display_name":"Soleiman Yousef","orcid":"https://orcid.org/0000-0003-2458-6264"},"institutions":[{"id":"https://openalex.org/I265217849","display_name":"IFP \u00c9nergies nouvelles","ror":"https://ror.org/03gcbhc33","country_code":"FR","type":"facility","lineage":["https://openalex.org/I265217849"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Soleiman Yousef","raw_affiliation_strings":["UPMC Universit\u00c3\u00a9, Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France \u00e2\u0080\u0093 and \u00e2\u0080\u0093 IFP Energies nouvelles, Department of Applied Mathematics, 1 & 4 avenue Bois Pr\u00c3\u00a9au, 92852 Rueil-Malmaison, France","Laboratoire Jacques-Louis Lions","IFP Energies nouvelles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UPMC Universit\u00c3\u00a9, Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France \u00e2\u0080\u0093 and \u00e2\u0080\u0093 IFP Energies nouvelles, Department of Applied Mathematics, 1 & 4 avenue Bois Pr\u00c3\u00a9au, 92852 Rueil-Malmaison, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I265217849","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]},{"raw_affiliation_string":"IFP Energies nouvelles","institution_ids":["https://openalex.org/I265217849"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5758,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.88325801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"84","issue":"291","first_page":"153","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6220881342887878},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3726050853729248},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36692726612091064}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6220881342887878},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3726050853729248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36692726612091064}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02854-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02854-8","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02854-8/S0025-5718-2014-02854-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.397.321","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397.321","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/82/94/37/PDF/Stefan.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.635.1747","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.635.1747","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal-ifp.archives-ouvertes.fr/docs/01/01/56/96/PDF/Di_Pietro-Vohralik-Yousef_2014.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00690862v4","is_oa":true,"landing_page_url":"https://hal.science/hal-00690862","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2015, 84 (291), pp.153--186. ⟨10.1090/S0025-5718-2014-02854-8⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2014-02854-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02854-8","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02854-8/S0025-5718-2014-02854-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322219","display_name":"IFP Energies Nouvelles","ror":"https://ror.org/03gcbhc33"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038393809.pdf","grobid_xml":"https://content.openalex.org/works/W2038393809.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W75674013","https://openalex.org/W100357283","https://openalex.org/W408406386","https://openalex.org/W1549748890","https://openalex.org/W1967011851","https://openalex.org/W1967764272","https://openalex.org/W1971606961","https://openalex.org/W1972684149","https://openalex.org/W1973784333","https://openalex.org/W1973874614","https://openalex.org/W1978926871","https://openalex.org/W1980377066","https://openalex.org/W1985554304","https://openalex.org/W1985642229","https://openalex.org/W1985911860","https://openalex.org/W1985988195","https://openalex.org/W1986783912","https://openalex.org/W1992184509","https://openalex.org/W2006443697","https://openalex.org/W2007289139","https://openalex.org/W2008683313","https://openalex.org/W2015788535","https://openalex.org/W2020004871","https://openalex.org/W2020292714","https://openalex.org/W2023111075","https://openalex.org/W2041523977","https://openalex.org/W2046128877","https://openalex.org/W2047378168","https://openalex.org/W2049561661","https://openalex.org/W2051269517","https://openalex.org/W2051889472","https://openalex.org/W2062438340","https://openalex.org/W2064265943","https://openalex.org/W2065900266","https://openalex.org/W2065980224","https://openalex.org/W2067951086","https://openalex.org/W2070623505","https://openalex.org/W2070753451","https://openalex.org/W2074006304","https://openalex.org/W2075388676","https://openalex.org/W2077322283","https://openalex.org/W2081063298","https://openalex.org/W2081954723","https://openalex.org/W2083027300","https://openalex.org/W2085677930","https://openalex.org/W2152799582","https://openalex.org/W2153299448","https://openalex.org/W2211676524","https://openalex.org/W2519971170","https://openalex.org/W2562668947","https://openalex.org/W3021722416","https://openalex.org/W3046787446","https://openalex.org/W4205438089","https://openalex.org/W4243944599","https://openalex.org/W4245552871","https://openalex.org/W4255525406","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"We":[0,205],"consider":[1],"in":[2],"this":[3],"paper":[4],"the":[5,30,37,57,61,67,102,105,149,157,175,187,200,208,227,232,241,258,264,267],"time-dependent":[6],"two-phase":[7],"Stefan":[8],"problem":[9],"and":[10,16,23,33,51,104,161,197,202,218,230,250,252,263],"derive":[11],"a":[12,49,179,183,223],"posteriori":[13],"error":[14,100,147,163],"estimates":[15,262],"adaptive":[17,166,268],"strategies":[18],"for":[19,186],"its":[20],"conforming":[21],"spatial":[22,201],"backward":[24],"Euler":[25],"temporal":[26,203],"discretizations.":[27],"Regularization":[28],"of":[29,36,40,60,101,148,178,199,210,226,231,260,266],"enthalpy-temperature":[31],"function":[32],"iterative":[34],"linearization":[35,162,188],"arising":[38],"systems":[39],"nonlinear":[41],"algebraic":[42],"equations":[43],"are":[44],"considered.":[45],"Our":[46,213],"estimators":[47],"yield":[48],"guaranteed":[50],"fully":[52],"computable":[53],"upper":[54,76,114],"bound":[55],"on":[56,66,222],"dual":[58],"norm":[59],"residual,":[62],"as":[63,65],"well":[64],"":[69,107],"":[79,120],"":[80,121],"":[81,122],"":[82,88,123,129],"L":[83,89,124],"2":[84,90,125],"":[85,91,126,138],"(":[87,128],"stretchy=\"false\">)":[93,140],"":[94,137,141],"L^2(L^2)":[96],"":[97,144],"":[98,145],"":[99,146],"temperature":[103],"H":[115],"Superscript":[116],"negative":[117],"1":[118],"Baseline":[119],"H":[130],"":[132],"":[133],"\u2212":[134],"":[135],"1":[136],"encoding=\"application/x-tex\">L^2(H^{-1})":[143],"enthalpy.":[150],"Moreover,":[151],"they":[152],"allow":[153],"us":[154],"to":[155,240],"distinguish":[156],"space,":[158],"time,":[159],"regularization,":[160],"components.":[164],"An":[165],"algorithm":[167],"is":[168,215,219],"proposed,":[169],"which":[170],"ensures":[171],"computational":[172],"savings":[173],"through":[174],"online":[176],"choice":[177,225],"sufficient":[180],"regularization":[181],"parameter,":[182],"stopping":[184],"criterion":[185],"iterations,":[189],"local":[190],"space":[191,228],"mesh":[192],"refinement,":[193],"time":[194],"step":[195],"adjustment,":[196],"equilibration":[198],"errors.":[204],"also":[206],"prove":[207],"efficiency":[209],"our":[211,261],"estimate.":[212],"analysis":[214],"quite":[216],"general":[217],"not":[220],"focused":[221],"specific":[224],"discretization":[229],"linearization.":[233],"As":[234],"an":[235],"example,":[236],"we":[237],"apply":[238],"it":[239],"vertex-centered":[242],"finite":[243],"volume":[244],"(finite":[245],"element":[246],"with":[247],"mass":[248],"lumping":[249],"quadrature)":[251],"Newton":[253],"methods.":[254],"Numerical":[255],"results":[256],"illustrate":[257],"effectiveness":[259],"performance":[265],"algorithm.":[269]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}