{"id":"https://openalex.org/W7214714787","doi":"https://doi.org/10.48550/arxiv.2609.31987","title":"Finite element error estimates for a bilinear optimal control problem with pointwise tracking governed by a semilinear elliptic PDE","display_name":"Finite element error estimates for a bilinear optimal control problem with pointwise tracking governed by a semilinear elliptic PDE","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214714787","doi":"https://doi.org/10.48550/arxiv.2609.31987"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31987","pdf_url":"https://arxiv.org/pdf/2609.31987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.31987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044773525","display_name":"Enrique Ot\u00e1rola D","orcid":"https://orcid.org/0000-0002-0812-5188","observed_orcids":["https://orcid.org/0000-0002-0812-5188"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Otarola, Enrique","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023756256","display_name":"Daniel Quero","orcid":"https://orcid.org/0009-0006-8525-1387","observed_orcids":["https://orcid.org/0009-0006-8525-1387"]},"institutions":[{"id":"https://openalex.org/I4210154195","display_name":"Universidad de Los Lagos","ror":"https://ror.org/05jk8e518","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210154195"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Quero, Daniel","raw_affiliation_strings":["Departamento de Ciencias Exactas , Universidad de Los Lagos , Osorno , Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ciencias Exactas , Universidad de Los Lagos , Osorno , Chile","institution_ids":["https://openalex.org/I4210154195"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5146928570","display_name":"Mat\u00edas Sasso","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sasso, Matias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":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":"Advanced Numerical Methods in Computational Mathematics","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/T11110","display_name":"Stability and Controllability of Differential Equations","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8579999804496765},{"id":"https://openalex.org/keywords/bilinear-control-systems","display_name":"bilinear control systems","score":0.8939999938011169},{"id":"https://openalex.org/keywords/semilinear-elliptic-equations","display_name":"semilinear elliptic equations","score":0.9879999756813049},{"id":"https://openalex.org/keywords/a-priori-error-estimates","display_name":"a priori error estimates","score":0.8109999895095825},{"id":"https://openalex.org/keywords/finite-element-discretization","display_name":"finite element discretization","score":0.8519999980926514},{"id":"https://openalex.org/keywords/semi-discrete-scheme","display_name":"semi-discrete scheme","score":0.9079999923706055},{"id":"https://openalex.org/keywords/fully-discrete-scheme","display_name":"fully discrete scheme","score":0.9929999709129333},{"id":"https://openalex.org/keywords/rate-constants","display_name":"rate constants","score":0.781000018119812},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.5479999780654907}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8360000252723694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7851999998092651},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7742999792098999},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7003999948501587},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6531000137329102},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5654000043869019},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5133000016212463},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.44530001282691956},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.36010000109672546},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33570000529289246},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.31349998712539673},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3068999946117401},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26409998536109924},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31987","pdf_url":"https://arxiv.org/pdf/2609.31987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.31987","doi":"https://doi.org/10.48550/arxiv.2609.31987","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31987","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.31987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31987","pdf_url":"https://arxiv.org/pdf/2609.31987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310976","display_name":"Universidad T\u00e9cnica Federico Santa Mar\u00eda","ror":"https://ror.org/05510vn56"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":"https://ror.org/05btm5233"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214714787.pdf","grobid_xml":"https://content.openalex.org/works/W7214714787.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3082555402","https://openalex.org/W2129060539","https://openalex.org/W2787514335","https://openalex.org/W4403301134","https://openalex.org/W2334875803","https://openalex.org/W2061822878","https://openalex.org/W1609576192","https://openalex.org/W2145302287","https://openalex.org/W2971392039","https://openalex.org/W1519165703"],"abstract_inverted_index":{"We":[0,46,131],"study":[1],"finite":[2],"element":[3],"approximations":[4],"for":[5,81,104,119,127],"an":[6],"optimal":[7,108],"control":[8,20,56,68],"problem":[9],"with":[10,133],"pointwise":[11],"tracking":[12],"governed":[13],"by":[14],"a":[15,27,32,51,62,92,106],"semilinear":[16],"elliptic":[17],"PDE.":[18],"The":[19],"variable":[21,57,69],"enters":[22],"the":[23,36,43,55,67,102,120,128,138,141],"state":[24,44],"equation":[25],"as":[26,98],"reaction":[28],"coefficient,":[29],"resulting":[30],"in":[31,101],"bilinear":[33],"control,":[34],"and":[35,61,78,90,124],"cost":[37],"functional":[38],"includes":[39],"point":[40],"evaluations":[41],"of":[42,87,140],"variable.":[45],"propose":[47],"two":[48,77,111],"discretization":[49],"schemes:":[50],"semidiscrete":[52,129],"scheme,":[53,65],"where":[54,66],"is":[58,70],"not":[59],"discretized,":[60],"fully":[63,121],"discrete":[64,88,122],"discretized":[71],"using":[72],"piecewise":[73],"constant":[74],"functions.":[75],"In":[76,110],"three":[79],"dimensions,":[80,112],"both":[82],"schemes,":[83],"we":[84],"establish":[85],"convergence":[86],"solutions":[89],"prove":[91],"priori":[93],"error":[94],"bounds":[95,114],"that":[96,136],"behave":[97],"$\\mathcal{O}(h|\\log":[99],"h|)$":[100],"$L^2(\u03a9)$-norm":[103],"approximating":[105],"locally":[107],"control.":[109],"these":[113],"are":[115],"improved":[116],"to":[117],"$\\mathcal{O}(h)$":[118],"scheme":[123],"$\\mathcal{O}(h^{2}|\\log":[125],"h|^2)$":[126],"scheme.":[130],"conclude":[132],"numerical":[134],"experiments":[135],"demonstrate":[137],"performance":[139],"proposed":[142],"schemes.":[143]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-30T00:00:00"}
