{"id":"https://openalex.org/W2943155467","doi":"https://doi.org/10.1007/s10915-019-00964-9","title":"A Priori Error Analysis for Time-Stepping Discontinuous Galerkin Finite Element Approximation of Time Fractional Optimal Control Problem","display_name":"A Priori Error Analysis for Time-Stepping Discontinuous Galerkin Finite Element Approximation of Time Fractional Optimal Control Problem","publication_year":2019,"publication_date":"2019-05-02","ids":{"openalex":"https://openalex.org/W2943155467","doi":"https://doi.org/10.1007/s10915-019-00964-9","mag":"2943155467"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-019-00964-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00964-9","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100337318","display_name":"Chenyang Zhang","orcid":"https://orcid.org/0000-0002-5806-2605"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenyang Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038663336","display_name":"Huipo Liu","orcid":"https://orcid.org/0000-0003-3591-4526"},"institutions":[{"id":"https://openalex.org/I4210145278","display_name":"Institute of Applied Physics and Computational Mathematics","ror":"https://ror.org/03sxpbt26","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210145278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huipo Liu","raw_affiliation_strings":["Institute of Applied Physics and Computational Mathematics, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Physics and Computational Mathematics, Beijing, China","institution_ids":["https://openalex.org/I4210145278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107961487","display_name":"Zhaojie Zhou","orcid":"https://orcid.org/0000-0003-0499-1545"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhaojie Zhou","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5107961487"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.4367,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8042654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"80","issue":"2","first_page":"993","last_page":"1018"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.8107435703277588},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7461823225021362},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7358976602554321},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6971001029014587},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.675582766532898},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5669893026351929},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5515739917755127},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5167078971862793},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48344096541404724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43199482560157776},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3093932569026947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15437310934066772}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8107435703277588},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7461823225021362},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7358976602554321},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6971001029014587},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.675582766532898},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5669893026351929},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5515739917755127},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5167078971862793},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48344096541404724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43199482560157776},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3093932569026947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15437310934066772},{"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":1,"locations":[{"id":"doi:10.1007/s10915-019-00964-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00964-9","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2890352925","display_name":null,"funder_award_id":"11301311","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4785020980","display_name":null,"funder_award_id":"ZR2016JL004","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G7947689107","display_name":"\u629b\u7269\u65b9\u7a0b\u6700\u4f18\u63a7\u5236\u95ee\u9898\u9ad8\u6548\u6709\u9650\u5143\u7b97\u6cd5\u53ca\u5176\u5728\u5206\u5b50\u6269\u6563\u8fc7\u7a0b\u7684\u5e94\u7528","funder_award_id":"11771053","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"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W642707038","https://openalex.org/W1483073639","https://openalex.org/W1600371943","https://openalex.org/W1607460358","https://openalex.org/W1966513244","https://openalex.org/W1971226930","https://openalex.org/W1981159109","https://openalex.org/W2053931412","https://openalex.org/W2082621526","https://openalex.org/W2093685032","https://openalex.org/W2127769310","https://openalex.org/W2132490216","https://openalex.org/W2139644578","https://openalex.org/W2172693370","https://openalex.org/W2191632485","https://openalex.org/W2319377454","https://openalex.org/W2408347580","https://openalex.org/W2476555123","https://openalex.org/W2529381973","https://openalex.org/W2545677352","https://openalex.org/W2768962672","https://openalex.org/W2771971878","https://openalex.org/W2787959293","https://openalex.org/W2889820468","https://openalex.org/W2963951614","https://openalex.org/W2964227878","https://openalex.org/W3145980692","https://openalex.org/W4248641565","https://openalex.org/W4255895408","https://openalex.org/W6600756316"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2055696851","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
