{"id":"https://openalex.org/W1974092704","doi":"https://doi.org/10.1109/iceee.2011.6106643","title":"Variational discretization and rectangle mixed finite element methods for quadratic semilinear elliptic optimal control problems","display_name":"Variational discretization and rectangle mixed finite element methods for quadratic semilinear elliptic optimal control problems","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W1974092704","doi":"https://doi.org/10.1109/iceee.2011.6106643","mag":"1974092704"},"language":"en","primary_location":{"id":"doi:10.1109/iceee.2011.6106643","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2011.6106643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control","raw_type":"proceedings-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/A5101570753","display_name":"Zuliang Lu","orcid":"https://orcid.org/0000-0003-3450-500X"},"institutions":[{"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"]},{"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":"Zuliang Lu","raw_affiliation_strings":["College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, China","School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, China","institution_ids":["https://openalex.org/I50180762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101570753"],"corresponding_institution_ids":["https://openalex.org/I4610292","https://openalex.org/I50180762"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06545475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"1","last_page":"5"},"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":0.9979000091552734,"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":0.9962999820709229,"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/rectangle","display_name":"Rectangle","score":0.8382309079170227},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8269007205963135},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7641148567199707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6911942958831787},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.585401177406311},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.563174307346344},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5529612302780151},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5516680479049683},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5206729173660278},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.449870765209198},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4475190043449402},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29276788234710693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14948031306266785},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08232313394546509}],"concepts":[{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.8382309079170227},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8269007205963135},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7641148567199707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6911942958831787},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.585401177406311},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.563174307346344},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5529612302780151},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5516680479049683},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5206729173660278},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.449870765209198},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4475190043449402},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29276788234710693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14948031306266785},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08232313394546509},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iceee.2011.6106643","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iceee.2011.6106643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320326217","display_name":"Hunan Provincial Innovation Foundation for Postgraduate","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W126240089","https://openalex.org/W1964479738","https://openalex.org/W1981159109","https://openalex.org/W1983113386","https://openalex.org/W1984479582","https://openalex.org/W1996289101","https://openalex.org/W2014245742","https://openalex.org/W2070959017","https://openalex.org/W2081350572","https://openalex.org/W2168552459","https://openalex.org/W2916947772","https://openalex.org/W3145980692","https://openalex.org/W4206443477","https://openalex.org/W4247005166"],"related_works":["https://openalex.org/W2242098268","https://openalex.org/W4244945894","https://openalex.org/W2760515006","https://openalex.org/W2802042052","https://openalex.org/W1987609185","https://openalex.org/W2003462717","https://openalex.org/W4224881918","https://openalex.org/W174828583","https://openalex.org/W2059098648","https://openalex.org/W2113133070"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"a":[5,60],"variational":[6],"discretization":[7],"and":[8,27,42,56],"rectangle":[9,37],"mixed":[10,38],"finite":[11,39],"element":[12,40],"methods":[13],"for":[14,53],"the":[15,28,33,43,54,67,71],"quadratic":[16],"optimal":[17],"control":[18,44,57],"problems":[19],"governed":[20],"by":[21,32],"semilinear":[22],"elliptic":[23],"equations.":[24],"The":[25],"state":[26,55],"co-state":[29],"are":[30,51],"approximated":[31],"lowest":[34],"order":[35,75],"Raviart-Thomas":[36],"spaces":[41],"is":[45,80],"not":[46],"discretized.":[47],"Optimal":[48],"error":[49],"estimates":[50],"established":[52],"variable.":[58],"As":[59],"result,":[61],"it":[62],"can":[63],"be":[64],"proved":[65],"that":[66],"discrete":[68],"solutions":[69],"possess":[70],"convergence":[72],"property":[73],"of":[74],"h.":[76],"A":[77],"numerical":[78],"example":[79],"presented":[81],"to":[82],"confirm":[83],"our":[84],"theoretical":[85],"results.":[86]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}