{"id":"https://openalex.org/W4383551032","doi":"https://doi.org/10.1007/s10915-023-02270-x","title":"Optimal-Order Convergence of a Two-Step BDF Method for the Navier\u2013Stokes Equations with $$H^1$$ Initial Data","display_name":"Optimal-Order Convergence of a Two-Step BDF Method for the Navier\u2013Stokes Equations with $$H^1$$ Initial Data","publication_year":2023,"publication_date":"2023-07-07","ids":{"openalex":"https://openalex.org/W4383551032","doi":"https://doi.org/10.1007/s10915-023-02270-x"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-023-02270-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-023-02270-x","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/A5110262704","display_name":"Tianyang Chu","orcid":null},"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":false,"raw_author_name":"Tianyang Chu","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024180528","display_name":"Jilu Wang","orcid":"https://orcid.org/0009-0001-9468-249X"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jilu Wang","raw_affiliation_strings":["School of Science, Harbin Institute of Technology, Shenzhen, 518055, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Harbin Institute of Technology, Shenzhen, 518055, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100461427","display_name":"Na Wang","orcid":"https://orcid.org/0000-0002-9786-8548"},"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":false,"raw_author_name":"Na Wang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China"],"raw_orcid":null,"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/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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA"],"raw_orcid":null,"affiliations":[{"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/A5024180528"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.387,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87970813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"96","issue":"2","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":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8642271161079407},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5874654650688171},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.565239667892456},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.5450766682624817},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5406242609024048},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5113560557365417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4936164617538452},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4837101101875305},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39541661739349365},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.15085071325302124},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06529006361961365}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8642271161079407},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5874654650688171},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.565239667892456},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.5450766682624817},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5406242609024048},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5113560557365417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4936164617538452},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4837101101875305},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39541661739349365},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.15085071325302124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06529006361961365},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/s10915-023-02270-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-023-02270-x","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/G608158488","display_name":null,"funder_award_id":"12071020, U2230402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6625624955","display_name":null,"funder_award_id":"12071020, 12131005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7794165260","display_name":null,"funder_award_id":"12131005","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":28,"referenced_works":["https://openalex.org/W1481633365","https://openalex.org/W1967343178","https://openalex.org/W1970564873","https://openalex.org/W1983119685","https://openalex.org/W1991242104","https://openalex.org/W1998271765","https://openalex.org/W2004168836","https://openalex.org/W2027822086","https://openalex.org/W2047859546","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2065874602","https://openalex.org/W2075872548","https://openalex.org/W2083680169","https://openalex.org/W2090708196","https://openalex.org/W2101743932","https://openalex.org/W2129758218","https://openalex.org/W2141886351","https://openalex.org/W2161229398","https://openalex.org/W2756774287","https://openalex.org/W2763611969","https://openalex.org/W2982020826","https://openalex.org/W3118262253","https://openalex.org/W3151605865","https://openalex.org/W3171386003","https://openalex.org/W3204708751","https://openalex.org/W4250690007","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2788247819","https://openalex.org/W2792440356","https://openalex.org/W3112745479","https://openalex.org/W4378474062","https://openalex.org/W4210855719","https://openalex.org/W1658046627"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}