{"id":"https://openalex.org/W3084022122","doi":"https://doi.org/10.1137/070679703","title":"A Legendre\u2013Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations","display_name":"A Legendre\u2013Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W3084022122","doi":"https://doi.org/10.1137/070679703","mag":"3084022122"},"language":"en","primary_location":{"id":"doi:10.1137/070679703","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679703","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yanping Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020948241","display_name":"Nianyu Yi","orcid":"https://orcid.org/0000-0002-2106-8237"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nianyu Yi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100373255","display_name":"Wenbin Liu","orcid":"https://orcid.org/0000-0002-4384-1446"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenbin Liu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038297858"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.1121,"has_fulltext":false,"cited_by_count":125,"citation_normalized_percentile":{"value":0.97015555,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"46","issue":"5","first_page":"2254","last_page":"2275"},"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":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.8688386678695679},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8505685329437256},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.8120224475860596},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7585930824279785},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7354539036750793},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5079694390296936},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5070726871490479},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.496004194021225},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4643111228942871},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4490903615951538},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3744037449359894},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32682135701179504},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2897629141807556},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12469401955604553}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8688386678695679},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8505685329437256},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.8120224475860596},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7585930824279785},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7354539036750793},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5079694390296936},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5070726871490479},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.496004194021225},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4643111228942871},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4490903615951538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3744037449359894},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32682135701179504},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2897629141807556},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12469401955604553},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070679703","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679703","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:kar.kent.ac.uk:22890","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/22890/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W201429281","https://openalex.org/W1543766063","https://openalex.org/W1974032925","https://openalex.org/W1995404822","https://openalex.org/W1997701847","https://openalex.org/W1998697817","https://openalex.org/W2006850990","https://openalex.org/W2009985306","https://openalex.org/W2014303698","https://openalex.org/W2018383942","https://openalex.org/W2029123910","https://openalex.org/W2030028670","https://openalex.org/W2039146619","https://openalex.org/W2047352485","https://openalex.org/W2053632598","https://openalex.org/W2082849992","https://openalex.org/W2093581986","https://openalex.org/W2410898212","https://openalex.org/W2495039291"],"related_works":["https://openalex.org/W2162026849","https://openalex.org/W2790191500","https://openalex.org/W3084022122","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W2365959816","https://openalex.org/W3048823941","https://openalex.org/W1976312688","https://openalex.org/W2020570337","https://openalex.org/W3024058709"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,23,39,42],"Legendre-Galerkin":[6],"spectral":[7,24],"approximation":[8,25],"for":[9,22,37],"a":[10,18,31],"constrained":[11],"optimal":[12,27],"control":[13,28,43],"problem.":[14],"We":[15],"first":[16],"derive":[17],"priori":[19],"error":[20,33],"estimates":[21,34],"of":[26],"problems.":[29],"Then":[30],"posteriori":[32],"are":[35],"obtained":[36],"both":[38],"state":[40],"and":[41],"approximation.":[44],"A":[45],"preconditioning":[46],"projection":[47],"algorithm":[48],"is":[49],"proposed":[50],"with":[51],"some":[52],"numerical":[53],"tests.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}