{"id":"https://openalex.org/W2019897249","doi":"https://doi.org/10.1137/s0036142996313580","title":"Convergence Analysis of a Finite Element Projection/Lagrange--Galerkin Method for the Incompressible Navier--Stokes Equations","display_name":"Convergence Analysis of a Finite Element Projection/Lagrange--Galerkin Method for the Incompressible Navier--Stokes Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2019897249","doi":"https://doi.org/10.1137/s0036142996313580","mag":"2019897249"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142996313580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142996313580","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/A5010896193","display_name":"Yves Achdou","orcid":"https://orcid.org/0000-0002-0514-3727"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. Achdou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045250454","display_name":"Jean\u2010Luc Guermond","orcid":"https://orcid.org/0000-0002-6974-6818"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. L. Guermond","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7737,"has_fulltext":false,"cited_by_count":127,"citation_normalized_percentile":{"value":0.88891939,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"37","issue":"3","first_page":"799","last_page":"826"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.849544882774353},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6501772999763489},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5958460569381714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5825752019882202},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5466093420982361},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.5274477601051331},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5164716243743896},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.508635401725769},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4460415244102478},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4229603111743927},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4165794551372528},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16472825407981873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06260091066360474}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849544882774353},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6501772999763489},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5958460569381714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5825752019882202},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5466093420982361},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.5274477601051331},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5164716243743896},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.508635401725769},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4460415244102478},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4229603111743927},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4165794551372528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16472825407981873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06260091066360474},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142996313580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142996313580","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":25,"referenced_works":["https://openalex.org/W42415071","https://openalex.org/W126871671","https://openalex.org/W202544164","https://openalex.org/W1593008802","https://openalex.org/W1674659126","https://openalex.org/W1708679080","https://openalex.org/W1967011851","https://openalex.org/W1988754720","https://openalex.org/W2002425660","https://openalex.org/W2021442667","https://openalex.org/W2024711466","https://openalex.org/W2028230944","https://openalex.org/W2031753395","https://openalex.org/W2036632883","https://openalex.org/W2047859546","https://openalex.org/W2051862019","https://openalex.org/W2056502139","https://openalex.org/W2062002217","https://openalex.org/W2076077791","https://openalex.org/W2090105604","https://openalex.org/W2091320748","https://openalex.org/W2477040106","https://openalex.org/W3043382640","https://openalex.org/W4285719527","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W4382469906","https://openalex.org/W1498017059","https://openalex.org/W2387870536","https://openalex.org/W2918697861","https://openalex.org/W1989607141","https://openalex.org/W4283775812","https://openalex.org/W4324275820","https://openalex.org/W92678590","https://openalex.org/W1980801980","https://openalex.org/W1703254095"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3,7,46,65],"convergence":[4],"analysis":[5],"of":[6,17,45,64,79,107,121,142],"fractional-step":[8],"method":[9,99],"to":[10],"compute":[11],"incompressible":[12],"viscous":[13],"flows":[14],"by":[15,43,62],"means":[16,44,63],"finite":[18,102],"element":[19],"approximations.":[20],"In":[21],"the":[22,25,27,30,50,53,73,85,90,97,112,116,126,130,134,139,143],"proposed":[23,98],"algorithm,":[24],"convection,":[26],"diffusion,":[28],"and":[29,52,87,118],"incompressibility":[31,54],"are":[32,55],"treated":[33,41,56],"in":[34,58,111,125],"three":[35],"different":[36],"substeps.":[37],"The":[38],"convection":[39],"is":[40,69,78,84,89,138],"first":[42],"Lagrange--Galerkin":[47],"technique,":[48],"whereas":[49],"diffusion":[51],"separately":[57],"two":[59],"subsequent":[60],"substeps":[61],"projection":[66],"method.":[67],"It":[68],"shown":[70],"that":[71],"provided":[72],"time":[74,103],"step,":[75],"$\\delta":[76],"t,$":[77],"${\\cal":[80,108,122],"O}(h^{d/4}),$":[81],"where":[82,136],"h":[83],"meshsize":[86],"d":[88,94],"space":[91],"dimension":[92],"($2\\leq":[93],"\\leq":[95],"3$),":[96],"yields":[100],"for":[101,115,133],"T":[104],"an":[105,119],"error":[106,120],"O}(h^{l+1}+\\delta":[109],"t)$":[110,124],"L2":[113,131],"norm":[114,128,132],"velocity":[117],"O}(h^{l}+\\delta":[123],"H1":[127],"(or":[129],"pressure),":[135],"l":[137],"polynomial":[140],"degree":[141],"approximate":[144],"velocity.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}