{"id":"https://openalex.org/W3135337288","doi":"https://doi.org/10.1137/20m1330452","title":"Unstructured Space-Time Finite Element Methods for Optimal Control of Parabolic Equations","display_name":"Unstructured Space-Time Finite Element Methods for Optimal Control of Parabolic Equations","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3135337288","doi":"https://doi.org/10.1137/20m1330452","mag":"3135337288"},"language":"en","primary_location":{"id":"doi:10.1137/20m1330452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1330452","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"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/A5058613122","display_name":"Ulrich Langer","orcid":"https://orcid.org/0000-0003-3797-7475"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ulrich Langer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037762950","display_name":"Olaf Steinbach","orcid":"https://orcid.org/0000-0002-2552-3022"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olaf Steinbach","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2552-3022","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082981580","display_name":"Fredi Tr\u00f6ltzsch","orcid":"https://orcid.org/0000-0002-7679-3233"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fredi Tr\u00f6ltzsch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014561752","display_name":"Huidong Yang","orcid":"https://orcid.org/0000-0001-8639-2030"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huidong Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2782,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95233746,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"A744","last_page":"A771"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976000189781189,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8027405738830566},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7864760160446167},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7169588804244995},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6862971782684326},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5977855920791626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5447503328323364},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.542932391166687},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.472394198179245},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41086408495903015},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3767431676387787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3628902733325958},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2527333199977875},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10662317276000977}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8027405738830566},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7864760160446167},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7169588804244995},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6862971782684326},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5977855920791626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5447503328323364},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.542932391166687},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.472394198179245},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41086408495903015},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3767431676387787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3628902733325958},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2527333199977875},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10662317276000977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1330452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1330452","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1572617741","https://openalex.org/W1991243721","https://openalex.org/W1993072133","https://openalex.org/W1994899657","https://openalex.org/W2008621392","https://openalex.org/W2009375605","https://openalex.org/W2015148405","https://openalex.org/W2030036911","https://openalex.org/W2031821805","https://openalex.org/W2051140339","https://openalex.org/W2060547843","https://openalex.org/W2061191702","https://openalex.org/W2074486210","https://openalex.org/W2076257978","https://openalex.org/W2091137920","https://openalex.org/W2093581986","https://openalex.org/W2139473935","https://openalex.org/W2168452183","https://openalex.org/W2287623205","https://openalex.org/W2345779166","https://openalex.org/W2402468387","https://openalex.org/W2527872183","https://openalex.org/W2532232939","https://openalex.org/W2727095630","https://openalex.org/W2789305006","https://openalex.org/W2789345946","https://openalex.org/W2939578506","https://openalex.org/W2996301385","https://openalex.org/W3000212964","https://openalex.org/W3105020391","https://openalex.org/W3165030955"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2006251942","https://openalex.org/W2087496541","https://openalex.org/W2108615321","https://openalex.org/W1984758362","https://openalex.org/W2085564391","https://openalex.org/W4388482258"],"abstract_inverted_index":{"This":[0,48],"work":[1],"presents":[2],"and":[3,54],"analyzes":[4],"space-time":[5,13,125],"finite":[6,126],"element":[7,127],"methods":[8],"on":[9,58,130,151],"fully":[10],"unstructured":[11],"simplicial":[12],"meshes":[14],"for":[15,35,51,103,123],"the":[16,31,77,98,104,135,152],"numerical":[17,119],"solution":[18],"of":[19,30],"parabolic":[20,71,143],"optimal":[21,72,144],"control":[22,46,73,145],"problems.":[23],"Using":[24],"Babu\u0161ka's":[25],"theorem,":[26],"we":[27,61,67,139],"show":[28],"well-posedness":[29],"first-order":[32,99],"optimality":[33,83,100],"systems":[34,101],"a":[36,69,91],"typical":[37],"model":[38,106],"problem":[39,74],"with":[40,147],"linear":[41,92,105],"state":[42],"equations,":[43],"but":[44],"without":[45],"constraints.":[47],"is":[49,85,95],"done":[50],"both":[52],"continuous":[53],"discrete":[55],"levels.":[56],"Based":[57],"these":[59],"results,":[60],"derive":[62],"discretization":[63],"error":[64,132],"estimates.":[65],"Then":[66],"consider":[68,141],"semilinear":[70,142],"arising":[75],"from":[76],"Schl\u00f6gl":[78],"model.":[79],"The":[80],"associated":[81],"nonlinear":[82],"system":[84],"solved":[86,111],"by":[87],"Newton's":[88],"method,":[89],"where":[90],"system,":[93],"which":[94],"similar":[96],"to":[97,109],"considered":[102],"problems,":[107],"has":[108],"be":[110],"at":[112],"each":[113],"Newton":[114],"step.":[115],"We":[116],"present":[117],"various":[118],"experiments":[120],"including":[121],"results":[122],"adaptive":[124],"discretizations":[128],"based":[129],"residual-type":[131],"indicators.":[133],"In":[134],"last":[136],"two":[137],"examples,":[138],"also":[140],"problems":[146],"box":[148],"constraints":[149],"imposed":[150],"control.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
