{"id":"https://openalex.org/W1992476771","doi":"https://doi.org/10.1007/s11424-011-9215-9","title":"L \u221e-estimates of mixed finite element methods for general nonlinear optimal control problems","display_name":"L \u221e-estimates of mixed finite element methods for general nonlinear optimal control problems","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W1992476771","doi":"https://doi.org/10.1007/s11424-011-9215-9","mag":"1992476771"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-011-9215-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-011-9215-9","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5038297858","display_name":"Yanping Chen","orcid":"https://orcid.org/0000-0002-7765-8201"},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanping Chen","raw_affiliation_strings":["School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China","SOUTH CHINA NORMAL UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China","institution_ids":["https://openalex.org/I187400657"]},{"raw_affiliation_string":"SOUTH CHINA NORMAL UNIVERSITY","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101570753","display_name":"Zuliang Lu","orcid":"https://orcid.org/0000-0003-3450-500X"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]},{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuliang Lu","raw_affiliation_strings":["College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, China","School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, China","Chongqing Three Gorges University","Xiangtan University"],"affiliations":[{"raw_affiliation_string":"College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, China","institution_ids":["https://openalex.org/I50180762"]},{"raw_affiliation_string":"Chongqing Three Gorges University","institution_ids":["https://openalex.org/I50180762"]},{"raw_affiliation_string":"Xiangtan University","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038297858"],"corresponding_institution_ids":["https://openalex.org/I187400657"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08109281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"1","first_page":"105","last_page":"120"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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":0.996999979019165,"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/pointwise","display_name":"Pointwise","score":0.8534021377563477},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7629551887512207},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.6818103790283203},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6428976655006409},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6096820831298828},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6094939708709717},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.568260908126831},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.5256876945495605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5226866006851196},{"id":"https://openalex.org/keywords/finite-element-limit-analysis","display_name":"Finite element limit analysis","score":0.46812689304351807},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.427796334028244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32915857434272766},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3169153332710266},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16301703453063965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08727410435676575}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8534021377563477},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7629551887512207},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.6818103790283203},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6428976655006409},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6096820831298828},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6094939708709717},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.568260908126831},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.5256876945495605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5226866006851196},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.46812689304351807},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.427796334028244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32915857434272766},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3169153332710266},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16301703453063965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08727410435676575},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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:10.1007/s11424-011-9215-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-011-9215-9","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/W56363010","https://openalex.org/W126240089","https://openalex.org/W136185420","https://openalex.org/W617279438","https://openalex.org/W959587680","https://openalex.org/W1483129574","https://openalex.org/W1543766063","https://openalex.org/W1708679080","https://openalex.org/W1980887896","https://openalex.org/W1981159109","https://openalex.org/W1984479582","https://openalex.org/W1996289101","https://openalex.org/W1996778903","https://openalex.org/W1998697817","https://openalex.org/W2005405969","https://openalex.org/W2009134079","https://openalex.org/W2014245742","https://openalex.org/W2014311013","https://openalex.org/W2021370156","https://openalex.org/W2031736379","https://openalex.org/W2031821805","https://openalex.org/W2036115869","https://openalex.org/W2067024715","https://openalex.org/W2081350572","https://openalex.org/W2091646309","https://openalex.org/W2157121531","https://openalex.org/W2597248869","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2367880982","https://openalex.org/W2350013512","https://openalex.org/W2021654023","https://openalex.org/W1573186872","https://openalex.org/W4254088695","https://openalex.org/W2134127411","https://openalex.org/W2185206193","https://openalex.org/W3196813885"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}