{"id":"https://openalex.org/W2890224601","doi":"https://doi.org/10.1007/s10915-018-0823-6","title":"Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints","display_name":"Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints","publication_year":2018,"publication_date":"2018-09-06","ids":{"openalex":"https://openalex.org/W2890224601","doi":"https://doi.org/10.1007/s10915-018-0823-6","mag":"2890224601"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0823-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0823-6","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://kar.kent.ac.uk/69853/1/2018-05-28-shen-state-constrain-elliptic.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025576158","display_name":"Wanfang Shen","orcid":"https://orcid.org/0000-0002-9534-3940"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wanfang Shen","raw_affiliation_strings":["School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I59483232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069736915","display_name":"Liang Ge","orcid":"https://orcid.org/0000-0001-5136-8081"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Ge","raw_affiliation_strings":["School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I34949971"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100373250","display_name":"Wenbin Liu","orcid":"https://orcid.org/0000-0001-9369-9858"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wenbin Liu","raw_affiliation_strings":["KBS, University of Kent, Canterbury, CT2 7PE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KBS, University of Kent, Canterbury, CT2 7PE, UK","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025576158"],"corresponding_institution_ids":["https://openalex.org/I59483232"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.0967278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"78","issue":"3","first_page":"1571","last_page":"1600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8555518388748169},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7041086554527283},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6374097466468811},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.585837185382843},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5694172978401184},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.5633146166801453},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5165947675704956},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4800892472267151},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4773723781108856},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.4545733630657196},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40596702694892883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23718127608299255},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2179773449897766},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.08319392800331116},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08027231693267822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8555518388748169},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7041086554527283},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6374097466468811},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.585837185382843},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5694172978401184},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.5633146166801453},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5165947675704956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4800892472267151},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4773723781108856},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.4545733630657196},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40596702694892883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23718127608299255},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2179773449897766},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.08319392800331116},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08027231693267822},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-018-0823-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0823-6","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:kar.kent.ac.uk:69853","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-0823-6>)","pdf_url":"https://kar.kent.ac.uk/69853/1/2018-05-28-shen-state-constrain-elliptic.pdf","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":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:kar.kent.ac.uk:69853","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-0823-6>)","pdf_url":"https://kar.kent.ac.uk/69853/1/2018-05-28-shen-state-constrain-elliptic.pdf","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":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3555861926","display_name":null,"funder_award_id":"11501326","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7916412652","display_name":null,"funder_award_id":"11701253","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2890224601.pdf","grobid_xml":"https://content.openalex.org/works/W2890224601.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W84648422","https://openalex.org/W571153997","https://openalex.org/W594510519","https://openalex.org/W1492326914","https://openalex.org/W1531883407","https://openalex.org/W1538934584","https://openalex.org/W1588974174","https://openalex.org/W1612723330","https://openalex.org/W1820125862","https://openalex.org/W1893779446","https://openalex.org/W1968573427","https://openalex.org/W1996088437","https://openalex.org/W2004515370","https://openalex.org/W2018159038","https://openalex.org/W2019529034","https://openalex.org/W2022977680","https://openalex.org/W2027362114","https://openalex.org/W2040905071","https://openalex.org/W2040960244","https://openalex.org/W2050874588","https://openalex.org/W2053632598","https://openalex.org/W2053931412","https://openalex.org/W2055460625","https://openalex.org/W2057523332","https://openalex.org/W2067780150","https://openalex.org/W2070530919","https://openalex.org/W2072205359","https://openalex.org/W2083845086","https://openalex.org/W2092622790","https://openalex.org/W2095505387","https://openalex.org/W2101552627","https://openalex.org/W2103452908","https://openalex.org/W2126193669","https://openalex.org/W2135329423","https://openalex.org/W2144865371","https://openalex.org/W2160520936","https://openalex.org/W2160786691","https://openalex.org/W2299439756","https://openalex.org/W2321957512","https://openalex.org/W2555558477","https://openalex.org/W2616506407","https://openalex.org/W2804099572","https://openalex.org/W2911730943","https://openalex.org/W2934526567","https://openalex.org/W3021722416","https://openalex.org/W3194721321","https://openalex.org/W4205634890","https://openalex.org/W4243961535","https://openalex.org/W4249667877","https://openalex.org/W4285719527","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W3031340132","https://openalex.org/W2783398617","https://openalex.org/W3033565194","https://openalex.org/W2104197120"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
