{"id":"https://openalex.org/W7124608051","doi":"https://doi.org/10.1007/s10915-026-03181-3","title":"The Lowest-Order Stabilized Virtual Element Method for the Evolutionary Navier-Stokes Equations with Small Viscosity","display_name":"The Lowest-Order Stabilized Virtual Element Method for the Evolutionary Navier-Stokes Equations with Small Viscosity","publication_year":2026,"publication_date":"2026-01-17","ids":{"openalex":"https://openalex.org/W7124608051","doi":"https://doi.org/10.1007/s10915-026-03181-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-026-03181-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-026-03181-3","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/A5123277570","display_name":"Xin Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Liu","raw_affiliation_strings":["MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi\u2019an, China","School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China","Xi\u2019an Key Laboratory of Scientific Computing and Applied Statistics, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Xi\u2019an Key Laboratory of Scientific Computing and Applied Statistics, Xi\u2019an, China","institution_ids":["https://openalex.org/I4210131919"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123284666","display_name":"Qixuan Song","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qixuan Song","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123277085","display_name":"Rui Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121011681","display_name":"Zhangxin Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]},{"id":"https://openalex.org/I4210165339","display_name":"Ningbo Institute of Industrial Technology","ror":"https://ror.org/05nqg3g04","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165339"]}],"countries":["CA","CN"],"is_corresponding":true,"raw_author_name":"Zhangxin Chen","raw_affiliation_strings":["Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, Alberta, Canada","Eastern Institute of Technology and Institute of Digital Twin, Ningbo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, Alberta, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Eastern Institute of Technology and Institute of Digital Twin, Ningbo, China","institution_ids":["https://openalex.org/I4210165339"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5121011681"],"corresponding_institution_ids":["https://openalex.org/I168635309","https://openalex.org/I4210165339"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08271917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"106","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":0.8672999739646912,"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":0.8672999739646912,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.03959999978542328,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.01730000041425228,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.7156999707221985},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.5647000074386597},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5199000239372253},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5040000081062317},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.48649999499320984},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4837000072002411},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.4555000066757202},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4410000145435333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8021000027656555},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7156999707221985},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.5647000074386597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5404000282287598},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5199000239372253},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.48649999499320984},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4837000072002411},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3377000093460083},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.28220000863075256},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C153919410","wikidata":"https://www.wikidata.org/wiki/Q9993851","display_name":"Weak formulation","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-026-03181-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-026-03181-3","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/G4530485338","display_name":null,"funder_award_id":"No.12371405","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W209576205","https://openalex.org/W1963803848","https://openalex.org/W1972100784","https://openalex.org/W1972368368","https://openalex.org/W1979899141","https://openalex.org/W1980659254","https://openalex.org/W1980781543","https://openalex.org/W1981944053","https://openalex.org/W1992896789","https://openalex.org/W1998338423","https://openalex.org/W2005632248","https://openalex.org/W2006000775","https://openalex.org/W2008635392","https://openalex.org/W2045686441","https://openalex.org/W2047049848","https://openalex.org/W2051751432","https://openalex.org/W2051862019","https://openalex.org/W2051984102","https://openalex.org/W2058241749","https://openalex.org/W2068845153","https://openalex.org/W2085620291","https://openalex.org/W2085999207","https://openalex.org/W2086422539","https://openalex.org/W2088357454","https://openalex.org/W2093922796","https://openalex.org/W2113267855","https://openalex.org/W2114670081","https://openalex.org/W2119859226","https://openalex.org/W2126548553","https://openalex.org/W2160623568","https://openalex.org/W2161530217","https://openalex.org/W2168914934","https://openalex.org/W2169575140","https://openalex.org/W2258832456","https://openalex.org/W2300243767","https://openalex.org/W2339371798","https://openalex.org/W2410416051","https://openalex.org/W2531452649","https://openalex.org/W2535353373","https://openalex.org/W2570090289","https://openalex.org/W2604714644","https://openalex.org/W2604774386","https://openalex.org/W2618791333","https://openalex.org/W2795226531","https://openalex.org/W2887442002","https://openalex.org/W2962917950","https://openalex.org/W2962924286","https://openalex.org/W2962939428","https://openalex.org/W2963008072","https://openalex.org/W2963131956","https://openalex.org/W2964307594","https://openalex.org/W2972627332","https://openalex.org/W2974757475","https://openalex.org/W2990554549","https://openalex.org/W3082484845","https://openalex.org/W3092307498","https://openalex.org/W3176597327","https://openalex.org/W3181119950","https://openalex.org/W3204708751","https://openalex.org/W3210035388","https://openalex.org/W3212880735","https://openalex.org/W4388636450","https://openalex.org/W4401065092"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-01-19T00:00:00"}
