{"id":"https://openalex.org/W2988504802","doi":"https://doi.org/10.1137/18m1231407","title":"Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity","display_name":"Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2988504802","doi":"https://doi.org/10.1137/18m1231407","mag":"2988504802"},"language":"en","primary_location":{"id":"doi:10.1137/18m1231407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1231407","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://duepublico2.uni-due.de/receive/duepublico_mods_00046818","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089722326","display_name":"Marco Winckler","orcid":"https://orcid.org/0000-0002-0756-6934"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Winckler","raw_affiliation_strings":["University of Duisburg-Essen, Fakult\u00e4t f\u00fcr Mathematik, Thea-Leymann-Str. 9, D-45127 Essen, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Duisburg-Essen, Fakult\u00e4t f\u00fcr Mathematik, Thea-Leymann-Str. 9, D-45127 Essen, Germany,","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000672190","display_name":"Irwin Yousept","orcid":"https://orcid.org/0000-0001-7315-501X"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"I. Yousept","raw_affiliation_strings":["University of Duisburg-Essen, Fakult\u00e4t f\u00fcr Mathematik, Thea-Leymann-Str. 9, D-45127 Essen, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Duisburg-Essen, Fakult\u00e4t f\u00fcr Mathematik, Thea-Leymann-Str. 9, D-45127 Essen, Germany,","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62318514"],"apc_list":null,"apc_paid":null,"fwci":1.5548,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79897027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"57","issue":"6","first_page":"2685","last_page":"2706"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9984999895095825,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.8092982172966003},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6281757354736328},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5366173982620239},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5103272795677185},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4824660122394562},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.4456862211227417},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.4410164952278137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4185425639152527}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8092982172966003},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6281757354736328},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5366173982620239},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5103272795677185},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4824660122394562},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.4456862211227417},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.4410164952278137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4185425639152527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1231407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1231407","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:duepublico2.uni-due.de:duepublico_mods_00046818","is_oa":true,"landing_page_url":"https://duepublico2.uni-due.de/receive/duepublico_mods_00046818","pdf_url":"https://duepublico2.uni-due.de/receive/duepublico_mods_00046818","source":{"id":"https://openalex.org/S4306400212","display_name":"DuEPublico (University of Duisburg-Essen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62318514","host_organization_name":"University of Duisburg-Essen","host_organization_lineage":["https://openalex.org/I62318514"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:duepublico2.uni-due.de:duepublico_mods_00046818","is_oa":true,"landing_page_url":"https://duepublico2.uni-due.de/receive/duepublico_mods_00046818","pdf_url":"https://duepublico2.uni-due.de/receive/duepublico_mods_00046818","source":{"id":"https://openalex.org/S4306400212","display_name":"DuEPublico (University of Duisburg-Essen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62318514","host_organization_name":"University of Duisburg-Essen","host_organization_lineage":["https://openalex.org/I62318514"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6015901424","display_name":null,"funder_award_id":"YO 159/2-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2988504802.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1973835324","https://openalex.org/W1983225957","https://openalex.org/W1997873767","https://openalex.org/W1998253133","https://openalex.org/W2010497258","https://openalex.org/W2017976561","https://openalex.org/W2042859897","https://openalex.org/W2043093781","https://openalex.org/W2057895638","https://openalex.org/W2061364127","https://openalex.org/W2061966864","https://openalex.org/W2062618977","https://openalex.org/W2071704402","https://openalex.org/W2071708379","https://openalex.org/W2095142041","https://openalex.org/W2141621517","https://openalex.org/W2141882285","https://openalex.org/W2141886996","https://openalex.org/W2143783905","https://openalex.org/W2152754773","https://openalex.org/W2161233730","https://openalex.org/W2205419184","https://openalex.org/W2235234346","https://openalex.org/W2621388823","https://openalex.org/W2739940524","https://openalex.org/W2763238702","https://openalex.org/W2768865607","https://openalex.org/W2963017886","https://openalex.org/W3027314990","https://openalex.org/W4231269780"],"related_works":["https://openalex.org/W2003080029","https://openalex.org/W3216871121","https://openalex.org/W3006957391","https://openalex.org/W1963948095","https://openalex.org/W3098480452","https://openalex.org/W2953368213","https://openalex.org/W2621388823","https://openalex.org/W2080111856","https://openalex.org/W4297068394","https://openalex.org/W2598737422"],"abstract_inverted_index":{"This":[0,99],"paper":[1,228,250],"considers":[2],"a":[3,48,60,89,113,166,194,233,238],"hyperbolic":[4],"Maxwell":[5,179],"variational":[6,97,180,197],"inequality":[7,181],"with":[8,112,157,182,201],"temperature":[9,21,183],"effects":[10],"arising":[11],"from":[12],"Bean's":[13],"critical-state":[14],"model":[15],"in":[16,25,57,63,171,199,264],"type-II":[17],"(high-temperature)":[18],"superconductivity.":[19,265],"Here,":[20],"dependence":[22],"is":[23,86,121,229],"included":[24],"the":[26,36,54,71,79,83,106,109,122,126,143,149,158,174,177,187,190,202,208,217,220,227,232,244,260],"critical":[27],"current":[28],"density":[29],"due":[30],"to":[31,104,164,215,231],"its":[32],"main":[33,119],"importance":[34],"for":[35,70,78,142,193],"realization":[37],"of":[38,66,108,125,136,148,176,189,219,226],"superconducting":[39],"effects,":[40],"as":[41],"confirmed":[42],"through":[43,186],"physical":[44,261],"measurements.":[45],"We":[46,247],"propose":[47],"fully":[49,128,150],"discrete":[50,110,129,151,195],"scheme":[51],"based":[52],"on":[53,243],"implicit":[55],"Euler":[56],"time":[58],"and":[59,74,145,207],"mixed":[61,196],"FEM":[62],"space":[64],"consisting":[65],"N\u00e9d\u00e9lec's":[67],"edge":[68],"elements":[69,77],"electric":[72,245],"field":[73],"piecewise":[75],"constant":[76],"magnetic":[80,115,204],"induction.":[81],"Furthermore,":[82],"initial":[84],"approximation":[85],"specified":[87],"by":[88,93,251],"compatibility":[90],"system":[91],"given":[92],"an":[94],"elliptic":[95],"curl-curl":[96],"inequality.":[98],"specific":[100],"setting":[101],"enables":[102],"us":[103,163],"derive":[105,165],"well-posedness":[107,175],"solution":[111,191],"certain":[114],"induction":[116,205],"regularity.":[117],"Our":[118],"result":[120],"uniform":[123,221],"convergence":[124,168,210],"proposed":[127],"method.":[130],"To":[131],"prove":[132],"this":[133,249],"result,":[134,169,211],"first":[135],"all,":[137],"we":[138,212],"establish":[139],"stability":[140,154],"estimates":[141,155],"zero-order":[144],"first-order":[146],"terms":[147],"solution.":[152],"These":[153],"along":[156],"underlying":[159],"nonlinear":[160],"structure":[161],"allow":[162],"weak-star":[167,209],"which":[170,257],"particular":[172],"yields":[173],"governing":[178],"effects.":[184],"Finally,":[185],"use":[188],"operator":[192],"problem":[198],"combination":[200],"involved":[203],"regularity":[206,241],"are":[213],"able":[214],"complete":[216],"proof":[218],"convergence.":[222],"The":[223],"last":[224],"part":[225],"devoted":[230],"priori":[234],"error":[235],"analysis":[236],"under":[237],"low":[239],"Sobolev":[240],"assumption":[242],"field.":[246],"close":[248],"presenting":[252],"some":[253],"three-dimensional":[254],"numerical":[255],"results,":[256],"especially":[258],"confirm":[259],"Meissner--Ochsenfeld":[262],"effect":[263]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}
