{"id":"https://openalex.org/W2025127681","doi":"https://doi.org/10.1137/080735369","title":"Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains","display_name":"Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2025127681","doi":"https://doi.org/10.1137/080735369","mag":"2025127681"},"language":"en","primary_location":{"id":"doi:10.1137/080735369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080735369","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/A5073230253","display_name":"Klaus Deckelnick","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klaus Deckelnick","raw_affiliation_strings":["klaus.deckelnick@mathematik.uni-magdeburg.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"klaus.deckelnick@mathematik.uni-magdeburg.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110044653","display_name":"Andreas G\u00fcnther","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas G\u00fcnther","raw_affiliation_strings":["andreas.guenther@math.uni-hamburg.de and michael.hinze@uni-hamburg.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"andreas.guenther@math.uni-hamburg.de and michael.hinze@uni-hamburg.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080919362","display_name":"Michael Hinze","orcid":"https://orcid.org/0000-0001-9688-0150"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Hinze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6363,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.97992415,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"48","issue":"4","first_page":"2798","last_page":"2819"},"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":0.9993000030517578,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9955000281333923,"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":0.8737238049507141},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8267821073532104},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.7172550559043884},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6509330868721008},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6369258165359497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5480596423149109},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5447337627410889},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.5035673975944519},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4996037483215332},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4930817782878876},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.48850691318511963},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4647224545478821},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4475557804107666},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4028114080429077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2305450141429901}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8737238049507141},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8267821073532104},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7172550559043884},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6509330868721008},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6369258165359497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5480596423149109},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5447337627410889},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.5035673975944519},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4996037483215332},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4930817782878876},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48850691318511963},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4647224545478821},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4475557804107666},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4028114080429077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2305450141429901},{"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":1,"locations":[{"id":"doi:10.1137/080735369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080735369","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1597209545","https://openalex.org/W1971226930","https://openalex.org/W1981159109","https://openalex.org/W1984337824","https://openalex.org/W1986476868","https://openalex.org/W2009985306","https://openalex.org/W2036893171","https://openalex.org/W2041304886","https://openalex.org/W2050097488","https://openalex.org/W2050178911","https://openalex.org/W2059975982","https://openalex.org/W2075330220","https://openalex.org/W2089167211","https://openalex.org/W2131839236","https://openalex.org/W2152932490"],"related_works":["https://openalex.org/W185197619","https://openalex.org/W5603432","https://openalex.org/W2988201549","https://openalex.org/W4307478649","https://openalex.org/W2150834087","https://openalex.org/W2517260436","https://openalex.org/W2036449252","https://openalex.org/W2342772136","https://openalex.org/W4300200796","https://openalex.org/W2184854647"],"abstract_inverted_index":{"We":[0,46,78],"consider":[1],"the":[2,14,52,71],"variational":[3],"discretization":[4],"of":[5],"elliptic":[6],"Dirichlet":[7],"optimal":[8,48,53],"control":[9,41,54],"problems":[10],"with":[11],"constraints":[12],"on":[13,23],"control.":[15],"The":[16,40],"underlying":[17,72],"state":[18],"equation,":[19],"which":[20],"is":[21,29,43],"considered":[22],"smooth":[24],"two-":[25],"and":[26,57,61],"three-dimensional":[27],"domains,":[28],"discretized":[30],"by":[31,83],"linear":[32],"finite":[33],"elements":[34],"taking":[35],"into":[36],"account":[37],"domain":[38],"approximation.":[39],"variable":[42],"not":[44],"discretized.":[45],"obtain":[47],"error":[49],"bounds":[50],"for":[51],"in":[55,66],"two":[56,67],"three":[58],"space":[59],"dimensions":[60],"prove":[62],"a":[63],"superconvergence":[64],"result":[65],"dimensions,":[68],"provided":[69],"that":[70],"mesh":[73],"satisfies":[74],"some":[75],"additional":[76],"condition.":[77],"confirm":[79],"our":[80],"analytical":[81],"findings":[82],"numerical":[84],"experiments.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
