{"id":"https://openalex.org/W2941043721","doi":"https://doi.org/10.1007/s10915-019-00943-0","title":"Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction","display_name":"Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction","publication_year":2019,"publication_date":"2019-03-22","ids":{"openalex":"https://openalex.org/W2941043721","doi":"https://doi.org/10.1007/s10915-019-00943-0","mag":"2941043721"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-019-00943-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00943-0","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":true,"raw_author_name":"Dongfang Li","raw_affiliation_strings":["Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 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, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 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/A5088646205","display_name":"Chengda Wu","orcid":"https://orcid.org/0000-0002-3490-9912"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Chengda Wu","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0002-3490-9912","affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073157317","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0009-0000-8778-7149"},"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":true,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, China","Department of Mathematics, Wayne State University, Detroit, USA","Beijing Computational Science Research Center, Beijing, 100193, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, USA","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073157317","https://openalex.org/A5088646205","https://openalex.org/A5100365824"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I185443292","https://openalex.org/I4210139958","https://openalex.org/I47720641"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":7.2636,"has_fulltext":false,"cited_by_count":119,"citation_normalized_percentile":{"value":0.97968044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"80","issue":"1","first_page":"403","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T10514","display_name":"Numerical methods in engineering","score":0.993399977684021,"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":0.8869417309761047},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6294592618942261},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5965254306793213},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5744581818580627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5638517737388611},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5442415475845337},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5417743921279907},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5282403826713562},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5053306221961975},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4903278648853302},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.46343618631362915},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4532791078090668},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4230729937553406},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18400922417640686}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8869417309761047},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6294592618942261},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5965254306793213},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5744581818580627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5638517737388611},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5442415475845337},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5417743921279907},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5282403826713562},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5053306221961975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4903278648853302},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.46343618631362915},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4532791078090668},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4230729937553406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18400922417640686},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-019-00943-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00943-0","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/G2093196656","display_name":null,"funder_award_id":"11726603","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/G4472046779","display_name":"\u82e5\u5e72\u5177\u6709\u5f31\u5bfc\u6570\u7684\u65b0\u578b\u8ba1\u7b97\u65b9\u6cd5\u7684\u68af\u5ea6\u91cd\u6784","funder_award_id":"11471031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4646362747","display_name":"\u7535\u78c1\u573a\u65b9\u7a0b\u53ca\u5176\u7279\u5f81\u503c\u95ee\u9898\u9ad8\u6548\u9ad8\u7cbe\u5ea6\u6570\u503c\u65b9\u6cd5","funder_award_id":"11871092","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"}],"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":43,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W646359550","https://openalex.org/W1544648253","https://openalex.org/W1584611818","https://openalex.org/W1965716945","https://openalex.org/W1967868847","https://openalex.org/W1976371327","https://openalex.org/W1998424577","https://openalex.org/W2005179009","https://openalex.org/W2034401440","https://openalex.org/W2041540906","https://openalex.org/W2062517214","https://openalex.org/W2070505112","https://openalex.org/W2073659542","https://openalex.org/W2082621526","https://openalex.org/W2088826361","https://openalex.org/W2151554918","https://openalex.org/W2220122545","https://openalex.org/W2278975655","https://openalex.org/W2299374223","https://openalex.org/W2510732450","https://openalex.org/W2535408367","https://openalex.org/W2560003211","https://openalex.org/W2588904077","https://openalex.org/W2593831893","https://openalex.org/W2601627861","https://openalex.org/W2608656286","https://openalex.org/W2619423951","https://openalex.org/W2624862304","https://openalex.org/W2751422907","https://openalex.org/W2752667287","https://openalex.org/W2778500870","https://openalex.org/W2781523636","https://openalex.org/W2783310902","https://openalex.org/W2792441096","https://openalex.org/W2799821673","https://openalex.org/W2804030256","https://openalex.org/W2806563100","https://openalex.org/W2916540042","https://openalex.org/W2963812646","https://openalex.org/W4211086183","https://openalex.org/W4242273588","https://openalex.org/W4245654886"],"related_works":["https://openalex.org/W4295815745","https://openalex.org/W2953079798","https://openalex.org/W1969674427","https://openalex.org/W3092754077","https://openalex.org/W1943927944","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W2161513111","https://openalex.org/W912076904"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":18}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}