{"id":"https://openalex.org/W2092498073","doi":"https://doi.org/10.1137/s0036142900373403","title":"A Fully Discrete Approximation for Control Problems Governed by Parabolic Variational Inequalities","display_name":"A Fully Discrete Approximation for Control Problems Governed by Parabolic Variational Inequalities","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2092498073","doi":"https://doi.org/10.1137/s0036142900373403","mag":"2092498073"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900373403","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900373403","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://inria.hal.science/inria-00072710","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014906860","display_name":"Ma\u0131\u0308tine Bergounioux","orcid":"https://orcid.org/0000-0001-7533-6957"},"institutions":[{"id":"https://openalex.org/I4210131315","display_name":"Laboratoire de Math\u00e9matiques Analyse, Probabilit\u00e9s, Mod\u00e9lisation Orl\u00e9ans","ror":"https://ror.org/03d6rdf69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I1294671590","https://openalex.org/I4210131315","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ma\u00eftine Bergounioux","raw_affiliation_strings":["Math\u00e9matiques - Analyse, Probabilit\u00e9s, Mod\u00e9lisation - Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques - Analyse, Probabilit\u00e9s, Mod\u00e9lisation - Orl\u00e9ans","institution_ids":["https://openalex.org/I4210131315"]}]},{"author_position":"last","author":{"id":null,"display_name":"Housnaa Zidani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164786","display_name":"Optimal Solutions (United States)","ror":"https://ror.org/05t1cnz26","country_code":"US","type":"company","lineage":["https://openalex.org/I4210164786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Housnaa Zidani","raw_affiliation_strings":["Methods of Optimal Control, Optimization and Applications"],"affiliations":[{"raw_affiliation_string":"Methods of Optimal Control, Optimization and Applications","institution_ids":["https://openalex.org/I4210164786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014906860"],"corresponding_institution_ids":["https://openalex.org/I4210131315"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.17078089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"39","issue":"6","first_page":"2014","last_page":"2033"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9994000196456909,"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/discretization","display_name":"Discretization","score":0.9024623036384583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8965544700622559},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.8134729266166687},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6742775440216064},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6290115714073181},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5204444527626038},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.507094144821167},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.49962806701660156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4957009553909302},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.45446768403053284},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4418891370296478},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43589261174201965},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27872341871261597}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.9024623036384583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8965544700622559},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8134729266166687},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6742775440216064},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6290115714073181},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5204444527626038},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.507094144821167},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.49962806701660156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4957009553909302},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.45446768403053284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4418891370296478},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43589261174201965},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27872341871261597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036142900373403","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900373403","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:HAL:hal-00022024v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00022024","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2002, 39, n\u00b06, pp.2014-2033","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-00990198v1","is_oa":false,"landing_page_url":"https://ensta-paris.hal.science/hal-00990198","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2002, 39 (6), pp.2014-2033. ⟨10.1137/S0036142900373403⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:inria-00072710v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00072710","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":"[Research Report] RR-3940, INRIA. 2000","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00072710v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00072710","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":"[Research Report] RR-3940, INRIA. 2000","raw_type":"Reports"},"sustainable_development_goals":[{"score":0.5799999833106995,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W38732339","https://openalex.org/W105615963","https://openalex.org/W144579591","https://openalex.org/W597907832","https://openalex.org/W1577322535","https://openalex.org/W1963664801","https://openalex.org/W1967755185","https://openalex.org/W1997717231","https://openalex.org/W2000334666","https://openalex.org/W2020896306","https://openalex.org/W2038626747","https://openalex.org/W2041523977","https://openalex.org/W2043971663","https://openalex.org/W2062618977","https://openalex.org/W2063560140","https://openalex.org/W2070621570","https://openalex.org/W2071596218","https://openalex.org/W2073584852","https://openalex.org/W2074190491","https://openalex.org/W2081550671","https://openalex.org/W2082621526","https://openalex.org/W2109168354","https://openalex.org/W4242273588"],"related_works":["https://openalex.org/W946352265","https://openalex.org/W2907092354","https://openalex.org/W2354852362","https://openalex.org/W2089955609","https://openalex.org/W2466040413","https://openalex.org/W2189596786","https://openalex.org/W3150056502","https://openalex.org/W2039299714","https://openalex.org/W4382053489","https://openalex.org/W2378504881"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3,41],"consider":[4],"a":[5,19],"numerical":[6],"approximation":[7],"of":[8],"an":[9],"optimal":[10],"control":[11],"problem":[12],"governed":[13],"by":[14],"variational":[15],"inequalities.":[16],"We":[17],"use":[18],"total":[20],"discretization":[21,25],"scheme:":[22],"implicit":[23],"Euler":[24],"with":[26],"respect":[27],"to":[28],"the":[29,37],"time":[30],"variable":[31],"and":[32,40],"finite":[33],"element":[34],"method":[35],"for":[36],"space":[38],"variable,":[39],"give":[42],"convergence":[43],"results.":[44]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}