{"id":"https://openalex.org/W1993575214","doi":"https://doi.org/10.1007/s11424-012-0279-y","title":"Variational discretization for parabolic optimal control problems with control constraints","display_name":"Variational discretization for parabolic optimal control problems with control constraints","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W1993575214","doi":"https://doi.org/10.1007/s11424-012-0279-y","mag":"1993575214"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-012-0279-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-012-0279-y","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/A5052121755","display_name":"Yuelong Tang","orcid":"https://orcid.org/0000-0001-8729-1098"},"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuelong Tang","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China","Xiangtan University"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"Xiangtan University","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","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":false,"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052121755"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0536,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75619583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"5","first_page":"880","last_page":"895"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9984999895095825,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9926999807357788,"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/discretization","display_name":"Discretization","score":0.8250020742416382},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7811534404754639},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7409541606903076},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6312136650085449},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5753477811813354},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5457252264022827},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4525347352027893},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4487369656562805},{"id":"https://openalex.org/keywords/left-and-right","display_name":"Left and right","score":0.4480594992637634},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.44493240118026733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44307205080986023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38158589601516724},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18697717785835266},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1703307032585144},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10459834337234497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10289719700813293}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8250020742416382},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7811534404754639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7409541606903076},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6312136650085449},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5753477811813354},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5457252264022827},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4525347352027893},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4487369656562805},{"id":"https://openalex.org/C2776719672","wikidata":"https://www.wikidata.org/wiki/Q17098435","display_name":"Left and right","level":2,"score":0.4480594992637634},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.44493240118026733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44307205080986023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38158589601516724},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18697717785835266},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1703307032585144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10459834337234497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10289719700813293},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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":1,"locations":[{"id":"doi:10.1007/s11424-012-0279-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-012-0279-y","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":19,"referenced_works":["https://openalex.org/W594510519","https://openalex.org/W1423703656","https://openalex.org/W1483129574","https://openalex.org/W1543766063","https://openalex.org/W1597209545","https://openalex.org/W1974032925","https://openalex.org/W1981159109","https://openalex.org/W2014303698","https://openalex.org/W2022977680","https://openalex.org/W2031821805","https://openalex.org/W2041523977","https://openalex.org/W2062936774","https://openalex.org/W2070959017","https://openalex.org/W2090721745","https://openalex.org/W2529381973","https://openalex.org/W3145980692","https://openalex.org/W4206443477","https://openalex.org/W4298228534","https://openalex.org/W4302819252"],"related_works":["https://openalex.org/W2080809482","https://openalex.org/W2064416388","https://openalex.org/W2378957471","https://openalex.org/W2119544289","https://openalex.org/W2075832483","https://openalex.org/W2001321943","https://openalex.org/W3165030955","https://openalex.org/W2008621392","https://openalex.org/W2081962455","https://openalex.org/W1993575214"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
