{"id":"https://openalex.org/W7137161620","doi":"https://doi.org/10.1007/s12190-026-02792-1","title":"A grad-div stabilized two-grid finite element discretization method for the steady natural convection equations","display_name":"A grad-div stabilized two-grid finite element discretization method for the steady natural convection equations","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7137161620","doi":"https://doi.org/10.1007/s12190-026-02792-1"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-026-02792-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-026-02792-1","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"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 Applied Mathematics and 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/A5129574759","display_name":"Duanquan Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Duanquan Zhou","raw_affiliation_strings":["School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People\u2019s Republic of China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129599820","display_name":"Bo Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I154893126","display_name":"Guizhou Normal University","ror":"https://ror.org/02x1pa065","country_code":"CN","type":"education","lineage":["https://openalex.org/I154893126"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zheng","raw_affiliation_strings":["School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, People\u2019s Republic of China","institution_ids":["https://openalex.org/I154893126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031706589","display_name":"Guoliang He","orcid":"https://orcid.org/0000-0003-2612-5023"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoliang He","raw_affiliation_strings":["School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, 610054, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, 610054, People\u2019s Republic of China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129584877","display_name":"Yueqiang Shang","orcid":null},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yueqiang Shang","raw_affiliation_strings":["School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People\u2019s Republic of China","institution_ids":["https://openalex.org/I142108993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031706589","https://openalex.org/A5129584877"],"corresponding_institution_ids":["https://openalex.org/I142108993","https://openalex.org/I150229711"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":4.9441,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.9285849,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"72","issue":"4","first_page":null,"last_page":null},"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":0.9614999890327454,"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":0.9614999890327454,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.009999999776482582,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.004900000058114529,"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/discretization","display_name":"Discretization","score":0.8025000095367432},{"id":"https://openalex.org/keywords/prandtl-number","display_name":"Prandtl number","score":0.71670001745224},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.6915000081062317},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6103000044822693},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49630001187324524},{"id":"https://openalex.org/keywords/rayleigh-number","display_name":"Rayleigh number","score":0.49630001187324524},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48570001125335693},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.44929999113082886}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8025000095367432},{"id":"https://openalex.org/C72687893","wikidata":"https://www.wikidata.org/wiki/Q815306","display_name":"Prandtl number","level":3,"score":0.71670001745224},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.6915000081062317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6559000015258789},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6103000044822693},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.49630001187324524},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49630001187324524},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4632999897003174},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4235999882221222},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.40070000290870667},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.39160001277923584},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.3192000091075897},{"id":"https://openalex.org/C46244369","wikidata":"https://www.wikidata.org/wiki/Q193709","display_name":"Rayleigh scattering","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C97346530","wikidata":"https://www.wikidata.org/wiki/Q487005","display_name":"Thermal conductivity","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-026-02792-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-026-02792-1","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"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 Applied Mathematics and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1964314926","https://openalex.org/W1974461496","https://openalex.org/W1979600419","https://openalex.org/W1980455776","https://openalex.org/W1987393363","https://openalex.org/W1989343938","https://openalex.org/W2001140395","https://openalex.org/W2017301866","https://openalex.org/W2017786109","https://openalex.org/W2032713536","https://openalex.org/W2041108136","https://openalex.org/W2041179520","https://openalex.org/W2043052949","https://openalex.org/W2043605704","https://openalex.org/W2059413295","https://openalex.org/W2061423965","https://openalex.org/W2070441252","https://openalex.org/W2082187902","https://openalex.org/W2095399846","https://openalex.org/W2111352333","https://openalex.org/W2134528122","https://openalex.org/W2135123656","https://openalex.org/W2142484159","https://openalex.org/W2154775388","https://openalex.org/W2159666799","https://openalex.org/W2164470476","https://openalex.org/W2460241900","https://openalex.org/W2480747491","https://openalex.org/W2535353373","https://openalex.org/W2545270568","https://openalex.org/W2593219174","https://openalex.org/W2744050773","https://openalex.org/W3164797527","https://openalex.org/W4211188765","https://openalex.org/W4252104256","https://openalex.org/W4311598740","https://openalex.org/W4392368869","https://openalex.org/W4396707025","https://openalex.org/W4400317902"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-03-17T00:00:00"}
