{"id":"https://openalex.org/W2792441096","doi":"https://doi.org/10.1007/s10915-018-0642-9","title":"Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction\u2013Subdiffusion Equations","display_name":"Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction\u2013Subdiffusion Equations","publication_year":2018,"publication_date":"2018-01-23","ids":{"openalex":"https://openalex.org/W2792441096","doi":"https://doi.org/10.1007/s10915-018-0642-9","mag":"2792441096"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0642-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0642-9","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/A5100365824","display_name":"Dongfang Li","orcid":"https://orcid.org/0000-0002-2901-3919"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongfang Li","raw_affiliation_strings":["Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353048","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0002-4493-7431"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiwei Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China"],"raw_orcid":"https://orcid.org/0000-0002-4493-7431","affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100406523","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-2704-6637"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China","Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100353048"],"corresponding_institution_ids":["https://openalex.org/I4210139958"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":6.1833,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.9730315,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"76","issue":"2","first_page":"848","last_page":"866"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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/mathematics","display_name":"Mathematics","score":0.8630511164665222},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6353837251663208},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6209747195243835},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.58228600025177},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5309312343597412},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5048461556434631},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5044304132461548},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.474700391292572},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4605599343776703},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44985660910606384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42056241631507874}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8630511164665222},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6353837251663208},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6209747195243835},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.58228600025177},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5309312343597412},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5048461556434631},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044304132461548},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.474700391292572},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4605599343776703},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44985660910606384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42056241631507874},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-018-0642-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0642-9","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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G1191030131","display_name":null,"funder_award_id":"11571128","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2746842099","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5405721928","display_name":null,"funder_award_id":"U1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5612984521","display_name":"\u51e0\u7c7b\u591a\u7ef4\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u9ad8\u6027\u80fd\u6570\u503c\u7b97\u6cd5\u7814\u7a76","funder_award_id":"11771162","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G890820059","display_name":null,"funder_award_id":"11771035","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W374977727","https://openalex.org/W1502589723","https://openalex.org/W1530054495","https://openalex.org/W1675532843","https://openalex.org/W1945420166","https://openalex.org/W1965716945","https://openalex.org/W1967868847","https://openalex.org/W1969399740","https://openalex.org/W1969547415","https://openalex.org/W1970546830","https://openalex.org/W1980154613","https://openalex.org/W1989867921","https://openalex.org/W2003202721","https://openalex.org/W2006043132","https://openalex.org/W2012437014","https://openalex.org/W2013596444","https://openalex.org/W2034401440","https://openalex.org/W2036215498","https://openalex.org/W2038300220","https://openalex.org/W2038588805","https://openalex.org/W2041523118","https://openalex.org/W2051862019","https://openalex.org/W2056829543","https://openalex.org/W2060650941","https://openalex.org/W2062517214","https://openalex.org/W2066415619","https://openalex.org/W2067889604","https://openalex.org/W2082621526","https://openalex.org/W2092942665","https://openalex.org/W2093685032","https://openalex.org/W2110719162","https://openalex.org/W2112360585","https://openalex.org/W2119671522","https://openalex.org/W2133004598","https://openalex.org/W2249797652","https://openalex.org/W2256853616","https://openalex.org/W2328902166","https://openalex.org/W2464719119","https://openalex.org/W2588904077","https://openalex.org/W2593831893","https://openalex.org/W2612471483","https://openalex.org/W2619423951","https://openalex.org/W2741724023","https://openalex.org/W2778500870","https://openalex.org/W2787959293","https://openalex.org/W2963309992","https://openalex.org/W3100645514","https://openalex.org/W3104329481","https://openalex.org/W4242273588","https://openalex.org/W6608498420"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1965109456","https://openalex.org/W2435162739","https://openalex.org/W2082446734","https://openalex.org/W2146736923","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2383733925","https://openalex.org/W2887215440"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":11}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}