{"id":"https://openalex.org/W2069726598","doi":"https://doi.org/10.1137/090746148","title":"A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints","display_name":"A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2069726598","doi":"https://doi.org/10.1137/090746148","mag":"2069726598"},"language":"en","primary_location":{"id":"doi:10.1137/090746148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090746148","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5053390954","display_name":"Klaus Krumbiegel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Krumbiegel","raw_affiliation_strings":["krumbieg@wias-berlin.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"krumbieg@wias-berlin.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037894286","display_name":"Christian Meyer","orcid":"https://orcid.org/0000-0003-3340-2316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Meyer","raw_affiliation_strings":["cmeyer@gsc.tu-darmstadt.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"cmeyer@gsc.tu-darmstadt.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073486661","display_name":"Arnd R\u00f6sch","orcid":"https://orcid.org/0009-0001-2163-7153"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. R\u00f6sch","raw_affiliation_strings":["arnd.roesch@uni-due.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"arnd.roesch@uni-due.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3456,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88637528,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"8","first_page":"5108","last_page":"5142"},"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":0.9998000264167786,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8115196824073792},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7301132082939148},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.729263424873352},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5744336843490601},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5250023603439331},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5174270868301392},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5026886463165283},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5000486373901367},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4910697937011719},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4809686243534088},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.47598543763160706},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4497343599796295},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43209007382392883},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3505675196647644},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.30201083421707153},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24708646535873413},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13480091094970703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11892956495285034},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07313305139541626}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8115196824073792},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7301132082939148},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.729263424873352},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5744336843490601},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5250023603439331},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5174270868301392},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5026886463165283},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5000486373901367},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4910697937011719},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4809686243534088},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.47598543763160706},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4497343599796295},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43209007382392883},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3505675196647644},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30201083421707153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24708646535873413},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13480091094970703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11892956495285034},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07313305139541626},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090746148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090746148","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W352877261","https://openalex.org/W1539280904","https://openalex.org/W1971226930","https://openalex.org/W1977135073","https://openalex.org/W1981159109","https://openalex.org/W1981611107","https://openalex.org/W1984337824","https://openalex.org/W1996088437","https://openalex.org/W2000450704","https://openalex.org/W2023628309","https://openalex.org/W2041304886","https://openalex.org/W2043391872","https://openalex.org/W2047599790","https://openalex.org/W2050097488","https://openalex.org/W2053931412","https://openalex.org/W2061822878","https://openalex.org/W2073110075","https://openalex.org/W2081146685","https://openalex.org/W2088908279","https://openalex.org/W2089828300","https://openalex.org/W2091525636","https://openalex.org/W2093626867","https://openalex.org/W2106853513","https://openalex.org/W2122106895","https://openalex.org/W2144865371","https://openalex.org/W2152932490","https://openalex.org/W2597248869","https://openalex.org/W4252219741"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2954004777","https://openalex.org/W2949638731","https://openalex.org/W2623997598","https://openalex.org/W3126543146"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"a":[5,29,34],"state-constrained":[6],"optimal":[7],"control":[8,54],"problem":[9],"with":[10,38],"boundary":[11],"control,":[12],"where":[13,52,59],"the":[14,47,50,53,57,60,66],"state":[15,61],"constraints":[16,62],"are":[17,63,73],"imposed":[18],"only":[19],"in":[20],"an":[21],"interior":[22],"subdomain.":[23],"Our":[24],"goal":[25],"is":[26],"to":[27],"derive":[28],"priori":[30],"error":[31],"estimates":[32],"for":[33],"finite":[35],"element":[36],"discretization":[37],"and":[39,56],"without":[40],"additional":[41],"regularization.":[42],"We":[43],"will":[44],"show":[45],"that":[46],"separation":[48],"of":[49],"set":[51,58],"acts":[55],"given":[64],"improves":[65],"approximation":[67],"rates":[68],"significantly.":[69],"The":[70],"theoretical":[71],"results":[72],"illustrated":[74],"by":[75],"numerical":[76],"computations.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
