{"id":"https://openalex.org/W1976803805","doi":"https://doi.org/10.2478/cmam-2011-0012","title":"Adaptive Finite Element Methods For Optimal Control Of Second Order Hyperbolic Equations","display_name":"Adaptive Finite Element Methods For Optimal Control Of Second Order Hyperbolic Equations","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1976803805","doi":"https://doi.org/10.2478/cmam-2011-0012","mag":"1976803805"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2011-0012","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2011-0012","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2011-0012/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2011-0012/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071446522","display_name":"Axel Kr\u00f6ner","orcid":null},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Axel Kr\u00f6ner","raw_affiliation_strings":["1Lehrstuhl f\u00fcr Mathematische Optimierung, Technische Universit\u00e4t M\u00fcnchen, Fakult\u00e4t f\u00fcr Mathematik, Boltzmannstra\u00dfe 3, 85748 Garching b. M\u00fcnchen, Germany","Technical University of Munich"],"affiliations":[{"raw_affiliation_string":"1Lehrstuhl f\u00fcr Mathematische Optimierung, Technische Universit\u00e4t M\u00fcnchen, Fakult\u00e4t f\u00fcr Mathematik, Boltzmannstra\u00dfe 3, 85748 Garching b. M\u00fcnchen, Germany","institution_ids":[]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071446522"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":2.1126,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.85838586,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"214","last_page":"240"},"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":0.9987000226974487,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9975000023841858,"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/finite-element-method","display_name":"Finite element method","score":0.7478012442588806},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7319344282150269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6812506914138794},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6510745286941528},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.6437674760818481},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5428909659385681},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5205175280570984},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5183433294296265},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5123730897903442},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4300501048564911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40490859746932983},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34794726967811584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09917023777961731},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.058384090662002563}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7478012442588806},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7319344282150269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6812506914138794},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6510745286941528},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.6437674760818481},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5428909659385681},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5205175280570984},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5183433294296265},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5123730897903442},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4300501048564911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40490859746932983},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34794726967811584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09917023777961731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.058384090662002563},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/cmam-2011-0012","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2011-0012","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2011-0012/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.303.5520","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.303.5520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/publications/reports/12/rep12-09.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.2478/cmam-2011-0012","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2011-0012","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2011-0012/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1976803805.pdf","grobid_xml":"https://content.openalex.org/works/W1976803805.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W46533625","https://openalex.org/W781224575","https://openalex.org/W1563812093","https://openalex.org/W1593553932","https://openalex.org/W1597209545","https://openalex.org/W1601728065","https://openalex.org/W1822954150","https://openalex.org/W1963847819","https://openalex.org/W1966027136","https://openalex.org/W1973841737","https://openalex.org/W1982378928","https://openalex.org/W1986596112","https://openalex.org/W1998967184","https://openalex.org/W2002985003","https://openalex.org/W2006309603","https://openalex.org/W2013519714","https://openalex.org/W2022977680","https://openalex.org/W2033517841","https://openalex.org/W2036884139","https://openalex.org/W2045354979","https://openalex.org/W2060546108","https://openalex.org/W2068610551","https://openalex.org/W2068874091","https://openalex.org/W2083310254","https://openalex.org/W2093572013","https://openalex.org/W2093581986","https://openalex.org/W2098101757","https://openalex.org/W2107753406","https://openalex.org/W2110485842","https://openalex.org/W2115494100","https://openalex.org/W2124471636","https://openalex.org/W2128722493","https://openalex.org/W2133147107","https://openalex.org/W2134431133","https://openalex.org/W2143455257","https://openalex.org/W2148192603","https://openalex.org/W2148631859","https://openalex.org/W2166320224","https://openalex.org/W2601853421","https://openalex.org/W3178415098","https://openalex.org/W4298356938","https://openalex.org/W4300184951","https://openalex.org/W6677741415","https://openalex.org/W6756173663","https://openalex.org/W6825962531"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W2163017860","https://openalex.org/W3162724489","https://openalex.org/W2356280110","https://openalex.org/W2017820475","https://openalex.org/W2058119626","https://openalex.org/W3149774417","https://openalex.org/W4254593442"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,74],"paper":[3],"we":[4,92],"consider":[5],"a":[6,50,57],"posteriori":[7,58],"error":[8,59],"estimates":[9,60],"for":[10,15],"space-time":[11],"finite":[12],"element":[13],"discretizations":[14],"optimal":[16,36],"control":[17,37,71],"of":[18,23,30,39,67,78,96,98],"hyperbolic":[19],"partial":[20],"dierential":[21],"equations":[22,41],"second":[24],"order.":[25],"It":[26],"is":[27,47,81],"an":[28],"extension":[29],"Meidner":[31],"and":[32,56,70],"Vexler":[33],"(2007),":[34],"where":[35],"problems":[38],"parabolic":[40],"are":[42,61,89],"analyzed.":[43],"The":[44],"state":[45],"equation":[46,102],"formulated":[48],"as":[49],"first":[51],"order":[52],"system":[53],"in":[54,65,107],"time":[55,108],"derived":[62],"separating":[63],"the":[64,76,79,94,99],"uences":[66],"time,":[68],"space,":[69],"discretization.":[72],"Using":[73],"information":[75],"accuracy":[77],"solution":[80],"improved":[82],"by":[83],"local":[84],"mesh":[85],"refinement.":[86],"Numerical":[87],"examples":[88],"presented.":[90],"Finally,":[91],"analyze":[93],"conservation":[95],"energy":[97],"homogeneous":[100],"wave":[101],"with":[103],"respect":[104],"to":[105],"dynamically":[106],"changing":[109],"spatial":[110],"meshes.":[111]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}