{"id":"https://openalex.org/W2909416950","doi":"https://doi.org/10.1007/s10589-020-00171-5","title":"Error estimates for the finite element approximation of bilinear boundary control problems","display_name":"Error estimates for the finite element approximation of bilinear boundary control problems","publication_year":2020,"publication_date":"2020-02-07","ids":{"openalex":"https://openalex.org/W2909416950","doi":"https://doi.org/10.1007/s10589-020-00171-5","mag":"2909416950"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-020-00171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-020-00171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-020-00171-5.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-020-00171-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041353339","display_name":"Max Winkler","orcid":"https://orcid.org/0000-0002-5292-2280"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Max Winkler","raw_affiliation_strings":["Faculty of Mathematics, Technische Universit\u00e4t Chemnitz, Chemnitz, Germany","Faculty of Mathematics Technische Universitat Chemnitz Chemnitz Germany"],"raw_orcid":"https://orcid.org/0000-0002-5292-2280","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technische Universit\u00e4t Chemnitz, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Faculty of Mathematics Technische Universitat Chemnitz Chemnitz Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041353339"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00433874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"76","issue":"1","first_page":"155","last_page":"199"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8925489187240601},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.791497528553009},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.62943434715271},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6122130155563354},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5848691463470459},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5516043901443481},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5389187335968018},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5089106559753418},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49043509364128113},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.41462013125419617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3999629318714142},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28222110867500305}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8925489187240601},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.791497528553009},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.62943434715271},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6122130155563354},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5848691463470459},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5516043901443481},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5389187335968018},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5089106559753418},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49043509364128113},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.41462013125419617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3999629318714142},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28222110867500305},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10589-020-00171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-020-00171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-020-00171-5.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.03612","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.03612","pdf_url":"https://arxiv.org/pdf/1901.03612","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2909416950","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1901.03612.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:spr:coopap:v:76:y:2020:i:1:d:10.1007_s10589-020-00171-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-020-00171-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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"},{"id":"pmh:oai:econstor.eu:10419/288485","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/288485","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"doi:10.48550/arxiv.1901.03612","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1901.03612","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10589-020-00171-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-020-00171-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-020-00171-5.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2909416950.pdf","grobid_xml":"https://content.openalex.org/works/W2909416950.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W591292934","https://openalex.org/W1516681311","https://openalex.org/W1586623601","https://openalex.org/W1799147386","https://openalex.org/W1971226930","https://openalex.org/W1981159109","https://openalex.org/W1981611107","https://openalex.org/W1988742883","https://openalex.org/W1996088437","https://openalex.org/W1999382308","https://openalex.org/W2005436751","https://openalex.org/W2009134079","https://openalex.org/W2009985306","https://openalex.org/W2012437014","https://openalex.org/W2031821805","https://openalex.org/W2035093248","https://openalex.org/W2045526409","https://openalex.org/W2046126451","https://openalex.org/W2052033235","https://openalex.org/W2058059020","https://openalex.org/W2059975982","https://openalex.org/W2061861714","https://openalex.org/W2065279412","https://openalex.org/W2069726598","https://openalex.org/W2129060539","https://openalex.org/W2244405571","https://openalex.org/W2297239611","https://openalex.org/W2523906455","https://openalex.org/W2538426691","https://openalex.org/W2597248869","https://openalex.org/W2609845013","https://openalex.org/W2789550572","https://openalex.org/W2792726437","https://openalex.org/W2897101154","https://openalex.org/W2963363042","https://openalex.org/W2964348923","https://openalex.org/W3204708751","https://openalex.org/W4234694874","https://openalex.org/W4245007249","https://openalex.org/W4250220742","https://openalex.org/W6600450457"],"related_works":["https://openalex.org/W3005516543","https://openalex.org/W2050357739","https://openalex.org/W2146814145","https://openalex.org/W2056498747","https://openalex.org/W3083799925","https://openalex.org/W3105802035","https://openalex.org/W3000234767","https://openalex.org/W3095927146","https://openalex.org/W1491346159","https://openalex.org/W2772859703","https://openalex.org/W2535239704","https://openalex.org/W2555558477","https://openalex.org/W2889820468","https://openalex.org/W1975677685","https://openalex.org/W2443207603","https://openalex.org/W2626714063","https://openalex.org/W2766289427","https://openalex.org/W2545677352","https://openalex.org/W3034077321","https://openalex.org/W2045082728"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article":[3],"a":[4,13,39,57,85,100],"special":[5],"class":[6],"of":[7,24,32,42,75,103,120],"nonlinear":[8],"optimal":[9,77],"control":[10,78,98],"problems":[11,25],"involving":[12],"bilinear":[14],"term":[15],"in":[16,29,53],"the":[17,30,43,47,72,76,89,104,118],"boundary":[18],"condition":[19],"is":[20,123],"studied.":[21],"These":[22],"kind":[23],"arise":[26],"for":[27,71],"instance":[28],"identification":[31],"an":[33,96],"unknown":[34],"space-dependent":[35],"Robin":[36,48],"coefficient":[37,49],"from":[38],"given":[40],"measurement":[41],"state,":[44],"or":[45],"when":[46],"can":[50],"be":[51],"controlled":[52],"order":[54],"to":[55],"reach":[56],"desired":[58],"state.":[59],"Necessary":[60],"and":[61,67,88,117],"sufficient":[62],"optimality":[63,106],"conditions":[64],"are":[65,80,83,115],"derived":[66],"several":[68],"discretization":[69,87],"approaches":[70,110],"numerical":[73,126],"solution":[74],"problem":[79],"investigated.":[81],"Considered":[82],"both":[84,109],"full":[86],"postprocessing":[90],"approach":[91],"meaning":[92],"that":[93],"we":[94],"compute":[95],"improved":[97],"by":[99,125],"pointwise":[101],"evaluation":[102],"first-order":[105],"condition.":[107],"For":[108],"finite":[111],"element":[112],"error":[113],"estimates":[114],"shown":[116],"validity":[119],"these":[121],"results":[122],"confirmed":[124],"experiments.":[127]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-07-30T00:00:00"}