{"id":"https://openalex.org/W2087987788","doi":"https://doi.org/10.1137/040607848","title":"Least-Squares Finite Element Methods for Optimality Systems Arising in Optimization and Control Problems","display_name":"Least-Squares Finite Element Methods for Optimality Systems Arising in Optimization and Control Problems","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2087987788","doi":"https://doi.org/10.1137/040607848","mag":"2087987788"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607848","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022276974","display_name":"Pavel Bochev","orcid":"https://orcid.org/0000-0002-8721-7119"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pavel Bochev","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max D. Gunzburger","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.388,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":21,"citation_normalized_percentile":{"value":0.752905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":88},"biblio":{"volume":"43","issue":"6","first_page":"2517","last_page":"2543"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Finite Element Methods for Fluid-Structure Interaction","score":1.0,"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":"Finite Element Methods for Fluid-Structure Interaction","score":1.0,"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":"Fracture Mechanics Modeling and Simulation","score":0.9985,"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/T11263","display_name":"Finite-Difference Time-Domain Methods in Electromagnetics","score":0.9979,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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-methods","display_name":"Finite Element Methods","score":0.554122},{"id":"https://openalex.org/keywords/discontinuous-galerkin-methods","display_name":"Discontinuous Galerkin Methods","score":0.524194},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended Finite Element Method","score":0.521979},{"id":"https://openalex.org/keywords/stabilized-methods","display_name":"Stabilized Methods","score":0.51098},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.47312897},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42054266}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.78510123},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7370521},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.65843767},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6114033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5157938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.51535815},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.50807667},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.49036407},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.47312897},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44992247},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42054266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20988944},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607848","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":26,"referenced_works":["https://openalex.org/W1607071030","https://openalex.org/W1674659126","https://openalex.org/W1708679080","https://openalex.org/W1965034652","https://openalex.org/W1977661241","https://openalex.org/W1987030962","https://openalex.org/W1994758810","https://openalex.org/W2008491645","https://openalex.org/W2022977680","https://openalex.org/W2050255334","https://openalex.org/W2051151419","https://openalex.org/W2055378644","https://openalex.org/W2059537627","https://openalex.org/W2065920748","https://openalex.org/W2071409656","https://openalex.org/W2077931396","https://openalex.org/W2099656682","https://openalex.org/W2168018853","https://openalex.org/W3143214667","https://openalex.org/W3149667697","https://openalex.org/W4240020390","https://openalex.org/W4250155727","https://openalex.org/W4251180451","https://openalex.org/W4252104256","https://openalex.org/W4298228534","https://openalex.org/W653136046"],"related_works":["https://openalex.org/W3177569183","https://openalex.org/W3123416417","https://openalex.org/W3032262642","https://openalex.org/W2950878479","https://openalex.org/W2889152090","https://openalex.org/W2474851184","https://openalex.org/W2409674212","https://openalex.org/W2389605564","https://openalex.org/W2370949144","https://openalex.org/W109887876"],"abstract_inverted_index":{"The":[0,78],"approximate":[1],"solution":[2,73,113],"of":[3,41,74,102,114,142],"optimization":[4,116,146],"and":[5,48,87,90],"optimal":[6,125],"control":[7],"problems":[8,21,147],"for":[9,71,108,128,148],"systems":[10],"governed":[11],"by":[12],"linear,":[13],"elliptic":[14],"partial":[15],"differential":[16],"equations":[17,80],"is":[18,98],"considered.":[19],"Such":[20],"are":[22,85,91],"most":[23],"often":[24],"solved":[25],"using":[26,65],"methods":[27,52,70,132],"based":[28],"on":[29],"applying":[30],"the":[31,42,72,75,115,143,149],"Lagrange":[32],"multiplier":[33],"rule":[34],"to":[35,54,94,134,145],"obtain":[36],"an":[37,45,99,120,140],"optimality":[38,49,76,135],"system":[39,56],"consisting":[40],"state":[43],"system,":[44,47],"adjoint-state":[46],"conditions.":[50],"Galerkin":[51],"applied":[53,133],"this":[55,83],"result":[57],"in":[58],"indefinite":[59],"matrix":[60,79],"problems.":[61],"Here,":[62],"we":[63],"consider":[64],"modern":[66],"least-squares":[67,103,129],"finite":[68,130],"element":[69,131],"systems.":[77,136],"resulting":[81],"from":[82],"approach":[84],"symmetric":[86],"positive":[88],"definite":[89],"readily":[92],"amenable":[93],"uncoupling":[95],"strategies.":[96],"This":[97],"important":[100],"advantage":[101],"principles":[104],"as":[105],"they":[106],"allow":[107],"a":[109],"more":[110],"efficient":[111],"computational":[112],"problem.":[117],"We":[118,137],"develop":[119],"abstract":[121],"theory":[122,144],"that":[123],"includes":[124],"error":[126],"estimates":[127],"then":[138],"provide":[139],"application":[141],"Stokes":[150],"equations.":[151]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2087987788","counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2024-09-30T05:53:14.058828","created_date":"2016-06-24"}
