{"id":"https://openalex.org/W3172282501","doi":"https://doi.org/10.1137/21m1443686","title":"An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier\u2013Stokes Equations","display_name":"An Arbitrary Order and Pointwise Divergence-Free Finite Element Scheme for the Incompressible 3D Navier\u2013Stokes Equations","publication_year":2023,"publication_date":"2023-04-24","ids":{"openalex":"https://openalex.org/W3172282501","doi":"https://doi.org/10.1137/21m1443686","mag":"3172282501"},"language":"en","primary_location":{"id":"doi:10.1137/21m1443686","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1443686","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.05146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029884193","display_name":"Marien-Lorenzo Hanot","orcid":"https://orcid.org/0000-0003-2579-9317"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marien-Lorenzo Hanot","raw_affiliation_strings":["IMAG, UMR 5149, Universit\u00e9 de Montpellier, 34090 Montpellier, France"],"raw_orcid":"https://orcid.org/0000-0003-2579-9317","affiliations":[{"raw_affiliation_string":"IMAG, UMR 5149, Universit\u00e9 de Montpellier, 34090 Montpellier, France","institution_ids":["https://openalex.org/I19894307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029884193"],"corresponding_institution_ids":["https://openalex.org/I19894307"],"apc_list":null,"apc_paid":null,"fwci":1.8635,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82073489,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"61","issue":"2","first_page":"784","last_page":"811"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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":0.9961000084877014,"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":0.8588101863861084},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.7797268629074097},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7699939012527466},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6725585460662842},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6324251890182495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.541254460811615},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.4604301154613495},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.43472611904144287},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3449419140815735}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8588101863861084},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7797268629074097},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7699939012527466},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6725585460662842},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6324251890182495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.541254460811615},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4604301154613495},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.43472611904144287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3449419140815735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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":3,"locations":[{"id":"doi:10.1137/21m1443686","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1443686","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"},{"id":"pmh:oai:arXiv.org:2106.05146","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.05146","pdf_url":"https://arxiv.org/pdf/2106.05146","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03250657v3","is_oa":true,"landing_page_url":"https://hal.science/hal-03250657","pdf_url":"https://hal.science/hal-03250657/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2023, 61 (2), pp.784-811. ⟨10.1137/21M1443686⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.05146","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.05146","pdf_url":"https://arxiv.org/pdf/2106.05146","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W278817411","https://openalex.org/W1674659126","https://openalex.org/W1972063580","https://openalex.org/W1981273084","https://openalex.org/W2003485525","https://openalex.org/W2007903663","https://openalex.org/W2034787856","https://openalex.org/W2106467688","https://openalex.org/W2131341034","https://openalex.org/W2135528252","https://openalex.org/W2142654352","https://openalex.org/W2143777332","https://openalex.org/W2155718237","https://openalex.org/W2166993143","https://openalex.org/W2196858524","https://openalex.org/W2507285513","https://openalex.org/W2744050773","https://openalex.org/W2801976144","https://openalex.org/W2906022956","https://openalex.org/W2964140071","https://openalex.org/W2969341892","https://openalex.org/W3028823202","https://openalex.org/W3102291936","https://openalex.org/W3103130136","https://openalex.org/W3103476862","https://openalex.org/W3135807520","https://openalex.org/W4245654886","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W2059881961","https://openalex.org/W2093607043","https://openalex.org/W1596838038","https://openalex.org/W2187142289","https://openalex.org/W2052669892","https://openalex.org/W2416979464","https://openalex.org/W2055092591","https://openalex.org/W2313597186","https://openalex.org/W1991751407","https://openalex.org/W2042362390"],"abstract_inverted_index":{"In":[0],"this":[1,67],"paper":[2],"we":[3,101],"discretize":[4],"the":[5,10,21,26,35,71,74,81,91],"incompressible":[6],"Navier-Stokes":[7],"equations":[8,27,98],"in":[9,60],"framework":[11],"of":[12,20,39,50,66,73,96],"finite":[13,51],"element":[14],"exterior":[15],"calculus.":[16],"We":[17,42,89],"make":[18],"use":[19],"Lamb":[22],"identity":[23],"to":[24],"rewrite":[25],"into":[28,34],"a":[29,44,47,94,106],"vorticity-velocity-pressure":[30],"form":[31],"which":[32,100],"fits":[33],"de":[36],"Rham":[37],"complex":[38],"minimal":[40],"regularity.":[41],"propose":[43],"discretization":[45,68],"on":[46,93],"large":[48],"class":[49,95],"elements,":[52],"including":[53],"arbitrary":[54],"order":[55],"polynomial":[56],"spaces":[57],"readily":[58],"available":[59],"many":[61],"libraries.":[62],"The":[63,110],"main":[64],"advantage":[65],"is":[69,77],"that":[70],"divergence":[72],"fluid":[75],"velocity":[76],"pointwise":[78],"zero":[79],"at":[80],"discrete":[82],"level.":[83],"This":[84],"exactness":[85],"ensures":[86],"pressure":[87],"robustness.":[88],"focus":[90],"analysis":[92],"linearized":[97],"for":[99],"prove":[102],"well-posedness":[103],"and":[104],"provide":[105],"priori":[107],"error":[108],"estimates.":[109],"results":[111],"are":[112],"validated":[113],"with":[114],"numerical":[115],"simulations.":[116]},"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":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}