{"id":"https://openalex.org/W2061795764","doi":"https://doi.org/10.1007/s00211-012-0462-z","title":"A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier\u2013Stokes equations","display_name":"A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier\u2013Stokes equations","publication_year":2012,"publication_date":"2012-03-13","ids":{"openalex":"https://openalex.org/W2061795764","doi":"https://doi.org/10.1007/s00211-012-0462-z","mag":"2061795764"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-012-0462-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-012-0462-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5100402579","display_name":"Jian Li","orcid":"https://orcid.org/0000-0003-1357-3089"},"institutions":[{"id":"https://openalex.org/I2799293361","display_name":"Baoji University of Arts and Sciences","ror":"https://ror.org/05nx0xs09","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799293361"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Li","raw_affiliation_strings":["Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, People\u2019s Republic of China","Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, People\u2019s Republic of China","institution_ids":["https://openalex.org/I2799293361"]},{"raw_affiliation_string":"Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, People's Republic of China","institution_ids":["https://openalex.org/I2799293361"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086480330","display_name":"Zhangxin Chen","orcid":"https://orcid.org/0000-0002-9107-1925"},"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/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Zhangxin Chen","raw_affiliation_strings":["Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People\u2019s Republic of China","Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Alberta, T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Alberta, T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100457891","display_name":"Yinnian He","orcid":"https://orcid.org/0000-0003-3402-8493"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinnian He","raw_affiliation_strings":["Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People\u2019s Republic of China","Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Center for Computational Geosciences, College of Mathematics and Statistics, Xian Jiaotong University, Xian, 710049, People's Republic of China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100402579"],"corresponding_institution_ids":["https://openalex.org/I2799293361"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.7785,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.89690999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"122","issue":"2","first_page":"279","last_page":"304"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.8584791421890259},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7977499961853027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7780987024307251},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6879326701164246},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6469173431396484},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6164321899414062},{"id":"https://openalex.org/keywords/finite-volume-method-for-one-dimensional-steady-state-diffusion","display_name":"Finite volume method for one-dimensional steady state diffusion","score":0.5970472693443298},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5581936240196228},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5057628154754639},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4979429244995117},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.471861332654953},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.44212764501571655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4297177493572235},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1554473340511322},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.11325034499168396},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.09650716185569763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09417745471000671},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.08232325315475464},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07506802678108215},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.057094722986221313},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.05266490578651428}],"concepts":[{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.8584791421890259},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7977499961853027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7780987024307251},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6879326701164246},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6469173431396484},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6164321899414062},{"id":"https://openalex.org/C85405225","wikidata":"https://www.wikidata.org/wiki/Q17013617","display_name":"Finite volume method for one-dimensional steady state diffusion","level":4,"score":0.5970472693443298},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5581936240196228},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5057628154754639},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4979429244995117},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.471861332654953},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.44212764501571655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4297177493572235},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1554473340511322},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.11325034499168396},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.09650716185569763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09417745471000671},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.08232325315475464},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07506802678108215},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.057094722986221313},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.05266490578651428},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-012-0462-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-012-0462-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/W100703333","https://openalex.org/W1521920611","https://openalex.org/W1582930900","https://openalex.org/W1674659126","https://openalex.org/W1967953674","https://openalex.org/W1969109739","https://openalex.org/W1970590191","https://openalex.org/W1974568345","https://openalex.org/W1975708402","https://openalex.org/W1980455776","https://openalex.org/W1984273492","https://openalex.org/W1985262947","https://openalex.org/W1986267641","https://openalex.org/W1986320166","https://openalex.org/W1986550841","https://openalex.org/W2017301866","https://openalex.org/W2017786109","https://openalex.org/W2022591932","https://openalex.org/W2023963475","https://openalex.org/W2029670554","https://openalex.org/W2034150466","https://openalex.org/W2041523977","https://openalex.org/W2041781096","https://openalex.org/W2043373580","https://openalex.org/W2046928485","https://openalex.org/W2051708601","https://openalex.org/W2057309217","https://openalex.org/W2067134767","https://openalex.org/W2076642757","https://openalex.org/W2089766265","https://openalex.org/W2091775502","https://openalex.org/W2119859226","https://openalex.org/W2121410213","https://openalex.org/W2477040106","https://openalex.org/W2511629455","https://openalex.org/W2884403958","https://openalex.org/W3143807873","https://openalex.org/W4210300254","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W1999000186","https://openalex.org/W2086666789","https://openalex.org/W2383924526","https://openalex.org/W2389068610","https://openalex.org/W2611733526","https://openalex.org/W2054873002","https://openalex.org/W2067743629","https://openalex.org/W4205474276","https://openalex.org/W2894062247","https://openalex.org/W1982893539"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}