{"id":"https://openalex.org/W1990165771","doi":"https://doi.org/10.1137/080718413","title":"Mixed Finite Element Methods for Incompressible Flow: Stationary Navier\u2013Stokes Equations","display_name":"Mixed Finite Element Methods for Incompressible Flow: Stationary Navier\u2013Stokes Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1990165771","doi":"https://doi.org/10.1137/080718413","mag":"1990165771"},"language":"en","primary_location":{"id":"doi:10.1137/080718413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080718413","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":["zcai@math.purdue.edu and cwang@math.purdue.edu and zhang@math.purdue.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"zcai@math.purdue.edu and cwang@math.purdue.edu and zhang@math.purdue.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101617085","display_name":"Chunbo Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chunbo Wang","raw_affiliation_strings":["Purdue University"],"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024697435","display_name":"Shun Zhang","orcid":"https://orcid.org/0000-0001-6235-0362"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shun Zhang","raw_affiliation_strings":["Purdue University"],"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023481731"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7289,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.8369332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"48","issue":"1","first_page":"79","last_page":"94"},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976000189781189,"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/mathematics","display_name":"Mathematics","score":0.8595802187919617},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7102031707763672},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7015539407730103},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6174319982528687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5914893746376038},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5273657441139221},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.48657071590423584},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.46454405784606934},{"id":"https://openalex.org/keywords/hagen\u2013poiseuille-flow-from-the-navier\u2013stokes-equations","display_name":"Hagen\u2013Poiseuille flow from the Navier\u2013Stokes equations","score":0.4621243476867676},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.42518261075019836},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.4206816554069519},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.37282246351242065},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2358379065990448},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09777465462684631},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06457176804542542}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8595802187919617},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7102031707763672},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7015539407730103},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6174319982528687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5914893746376038},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5273657441139221},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.48657071590423584},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.46454405784606934},{"id":"https://openalex.org/C66540979","wikidata":"https://www.wikidata.org/wiki/Q869854","display_name":"Hagen\u2013Poiseuille flow from the Navier\u2013Stokes equations","level":4,"score":0.4621243476867676},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.42518261075019836},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.4206816554069519},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.37282246351242065},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2358379065990448},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09777465462684631},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06457176804542542},{"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:10.1137/080718413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080718413","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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":37,"referenced_works":["https://openalex.org/W5800307","https://openalex.org/W136185420","https://openalex.org/W1492326914","https://openalex.org/W1533889494","https://openalex.org/W1582930900","https://openalex.org/W1595604189","https://openalex.org/W1634938045","https://openalex.org/W1674659126","https://openalex.org/W1708679080","https://openalex.org/W1852082788","https://openalex.org/W1969838226","https://openalex.org/W1976140148","https://openalex.org/W1981407574","https://openalex.org/W1999331305","https://openalex.org/W2004683822","https://openalex.org/W2006617763","https://openalex.org/W2008004031","https://openalex.org/W2014744421","https://openalex.org/W2026991963","https://openalex.org/W2033986961","https://openalex.org/W2036115869","https://openalex.org/W2041523977","https://openalex.org/W2049314152","https://openalex.org/W2051682834","https://openalex.org/W2073370369","https://openalex.org/W2075896209","https://openalex.org/W2079318234","https://openalex.org/W2083040919","https://openalex.org/W2100858486","https://openalex.org/W2147446841","https://openalex.org/W2167444171","https://openalex.org/W2277677093","https://openalex.org/W2592623476","https://openalex.org/W2884403958","https://openalex.org/W3148800415","https://openalex.org/W3149667697","https://openalex.org/W3204708751"],"related_works":["https://openalex.org/W2806285043","https://openalex.org/W2042362390","https://openalex.org/W1823475116","https://openalex.org/W2500173965","https://openalex.org/W1991751407","https://openalex.org/W2319762806","https://openalex.org/W2038540943","https://openalex.org/W2025976269","https://openalex.org/W265525530","https://openalex.org/W1632850910"],"abstract_inverted_index":{"In":[0],"[Z.":[1],"Cai,":[2],"C.":[3,9],"Tong,":[4],"P.":[5],"S.":[6],"Vassilevski,":[7],"and":[8,21,40,57,89,98],"Wang,":[10],"Numer.":[11],"Methods":[12],"Partial":[13],"Differential":[14],"Equations,":[15],"to":[16,70],"appear],":[17],"the":[18,29,35,41,68,71,82,86,102],"authors":[19],"developed":[20],"analyzed":[22],"a":[23,46],"mixed":[24,103],"finite":[25,50,104],"element":[26,105],"method":[27,69],"for":[28],"stationary":[30],"Stokes":[31],"equations":[32],"based":[33],"on":[34],"pseudostress-velocity":[36,83],"formulation.":[37],"The":[38],"pseudostress":[39],"velocity":[42],"are":[43,107],"approximated":[44],"by":[45],"stable":[47],"pair":[48],"of":[49,54,61,85,95,101],"elements:":[51],"Raviart\u2013Thomas":[52],"elements":[53],"index":[55],"$k\\geq0$":[56],"discontinuous":[58],"piecewise":[59],"polynomials":[60],"degree":[62],"$k\\geq0$,":[63],"respectively.":[64],"This":[65],"paper":[66],"extends":[67],"stationary,":[72],"incompressible":[73],"Navier\u2013Stokes":[74,87],"equations.":[75],"Under":[76],"appropriate":[77],"assumptions,":[78],"we":[79],"show":[80],"that":[81],"formulation":[84],"equation":[88],"its":[90],"discrete":[91],"counterpart":[92],"have":[93],"branches":[94],"nonsingular":[96],"solutions,":[97],"error":[99],"estimates":[100],"approximations":[106],"established":[108],"as":[109],"well.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-04T09:10:02.777135","created_date":"2025-10-10T00:00:00"}
