{"id":"https://openalex.org/W4414139137","doi":"https://doi.org/10.1007/s00211-025-01490-7","title":"Numerical analysis for Dirichlet optimal control problems on convex polyhedral domains","display_name":"Numerical analysis for Dirichlet optimal control problems on convex polyhedral domains","publication_year":2025,"publication_date":"2025-09-11","ids":{"openalex":"https://openalex.org/W4414139137","doi":"https://doi.org/10.1007/s00211-025-01490-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-025-01490-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01490-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01490-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01490-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013353521","display_name":"Johannes Pfefferer","orcid":null},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Johannes Pfefferer","raw_affiliation_strings":["Department of Electrical Power Systems and Information Technology, University of the Bundeswehr Munich, Neubiberg, Germany","Department of Electrical Power Systems and Information Technology, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85579, Neubiberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Power Systems and Information Technology, University of the Bundeswehr Munich, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]},{"raw_affiliation_string":"Department of Electrical Power Systems and Information Technology, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85579, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085823095","display_name":"Boris Vexler","orcid":"https://orcid.org/0000-0001-6211-4263"},"institutions":[{"id":"https://openalex.org/I4210090447","display_name":"Kutaisi International University","ror":"https://ror.org/017fspt77","country_code":"GE","type":"education","lineage":["https://openalex.org/I4210090447"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE","GE"],"is_corresponding":true,"raw_author_name":"Boris Vexler","raw_affiliation_strings":["School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, Garching by Munich, Germany","School of Mathematics, Kutaisi International University, Kutaisi, Georgia","School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, Boltzmannstr. 3, 85748, Garching by Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, Garching by Munich, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"School of Mathematics, Kutaisi International University, Kutaisi, Georgia","institution_ids":["https://openalex.org/I4210090447"]},{"raw_affiliation_string":"School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, Boltzmannstr. 3, 85748, Garching by Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013353521","https://openalex.org/A5085823095"],"corresponding_institution_ids":["https://openalex.org/I40527276","https://openalex.org/I4210090447","https://openalex.org/I62916508"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.3233,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7852231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"157","issue":"5","first_page":"1937","last_page":"1974"},"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":0.9991000294685364,"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"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/discretization","display_name":"Discretization","score":0.7365000247955322},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.6572999954223633},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.586899995803833},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5723000168800354},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.5541999936103821},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5091000199317932},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.49239999055862427},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4885999858379364},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4884999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8694999814033508},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7365000247955322},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6572999954223633},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.586899995803833},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5723000168800354},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.5541999936103821},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5091000199317932},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.49239999055862427},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4884999990463257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48669999837875366},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43709999322891235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41620001196861267},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.3815000057220459},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.31299999356269836},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.28839999437332153},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.28760001063346863},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28040000796318054},{"id":"https://openalex.org/C58385900","wikidata":"https://www.wikidata.org/wiki/Q5347254","display_name":"Effective domain","level":5,"score":0.2766999900341034},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-025-01490-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01490-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01490-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-025-01490-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01490-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01490-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414139137.pdf","grobid_xml":"https://content.openalex.org/works/W4414139137.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W44035921","https://openalex.org/W89839489","https://openalex.org/W1480363740","https://openalex.org/W1492085189","https://openalex.org/W1498345005","https://openalex.org/W1586623601","https://openalex.org/W1965332272","https://openalex.org/W1968608557","https://openalex.org/W1971226930","https://openalex.org/W1981159109","https://openalex.org/W1989318802","https://openalex.org/W1999382308","https://openalex.org/W2010207646","https://openalex.org/W2025127681","https://openalex.org/W2041304886","https://openalex.org/W2050097488","https://openalex.org/W2051043245","https://openalex.org/W2053085169","https://openalex.org/W2053482768","https://openalex.org/W2064322993","https://openalex.org/W2067267383","https://openalex.org/W2132729901","https://openalex.org/W2138797360","https://openalex.org/W2152932490","https://openalex.org/W2306359540","https://openalex.org/W2461866128","https://openalex.org/W2611709087","https://openalex.org/W2745572829","https://openalex.org/W2790726926","https://openalex.org/W2962921361","https://openalex.org/W2993719487","https://openalex.org/W3098683700","https://openalex.org/W3102419064","https://openalex.org/W3174503691","https://openalex.org/W3204708751","https://openalex.org/W4245007249","https://openalex.org/W4410168163"],"related_works":["https://openalex.org/W1892002403","https://openalex.org/W4309005041","https://openalex.org/W2962746246","https://openalex.org/W1989531755","https://openalex.org/W1967384683","https://openalex.org/W1523912116","https://openalex.org/W1975406625","https://openalex.org/W4300200796","https://openalex.org/W11313543","https://openalex.org/W2184854647"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"error":[4,23],"analysis":[5],"for":[6,56],"finite":[7],"element":[8],"discretizations":[9],"of":[10,30,45],"Dirichlet":[11],"boundary":[12],"control":[13],"problems":[14],"is":[15],"developed.":[16],"For":[17],"the":[18,28,43,57,62,65],"first":[19],"time,":[20],"optimal":[21],"discretization":[22],"estimates":[24],"are":[25,52,69,84],"established":[26],"in":[27],"case":[29],"three":[31],"dimensional":[32,59,67],"polyhedral":[33],"and":[34],"convex":[35],"domains.":[36],"The":[37,81],"convergence":[38],"rates":[39],"solely":[40],"depend":[41],"on":[42],"size":[44],"largest":[46],"interior":[47],"edge":[48],"angle.":[49],"These":[50],"results":[51,83],"comparable":[53],"to":[54,78],"those":[55],"two":[58,66],"case.":[60],"However,":[61],"approaches":[63],"from":[64],"setting":[68],"not":[70],"directly":[71],"extendable":[72],"such":[73],"that":[74],"new":[75],"techniques":[76],"have":[77],"be":[79],"used.":[80],"theoretical":[82],"confirmed":[85],"by":[86],"numerical":[87],"experiments.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
