{"id":"https://openalex.org/W2905420259","doi":"https://doi.org/10.1137/18m1177688","title":"A Quasi-optimal Crouzeix--Raviart Discretization of the Stokes Equations","display_name":"A Quasi-optimal Crouzeix--Raviart Discretization of the Stokes Equations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2905420259","doi":"https://doi.org/10.1137/18m1177688","mag":"2905420259"},"language":"en","primary_location":{"id":"doi:10.1137/18m1177688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177688","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1812.04889","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020163821","display_name":"R. Verf\u00fcrth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R\u00fcdiger Verf\u00fcrth","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7355-427X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039437637","display_name":"Pietro Zanotti","orcid":"https://orcid.org/0000-0003-4505-3520"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pietro Zanotti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.009334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"3","first_page":"1082","last_page":"1099"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9954000115394592,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9912999868392944,"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/solenoidal-vector-field","display_name":"Solenoidal vector field","score":0.8663281202316284},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7068372964859009},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.696031928062439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6805908679962158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.553433895111084},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.527164876461029},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5046976804733276},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.47427377104759216},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15305498242378235},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10307210683822632}],"concepts":[{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.8663281202316284},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7068372964859009},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.696031928062439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6805908679962158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.553433895111084},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.527164876461029},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5046976804733276},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.47427377104759216},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15305498242378235},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10307210683822632},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/18m1177688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177688","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:1812.04889","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.04889","pdf_url":"https://arxiv.org/pdf/1812.04889","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1812.04889","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1812.04889","pdf_url":"https://arxiv.org/pdf/1812.04889","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"mag:2905420259","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1812.04889v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eldorado.tu-dortmund.de:2003/37838","is_oa":false,"landing_page_url":"http://hdl.handle.net/2003/37838","pdf_url":null,"source":{"id":"https://openalex.org/S4377196631","display_name":"Eldorado - Repository of the TU Dortmund (TU Dortmund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200332995","host_organization_name":"TU Dortmund University","host_organization_lineage":["https://openalex.org/I200332995"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:preprint"},{"id":"doi:10.48550/arxiv.1812.04889","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1812.04889","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.17877/de290r-19833","is_oa":true,"landing_page_url":"https://doi.org/10.17877/de290r-19833","pdf_url":null,"source":{"id":"https://openalex.org/S4306400811","display_name":"Technische Universit\u00e4t Dortmund Eldorado (Technische Universit\u00e4t Dortmund)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210148506","host_organization_name":"Erich-Brost-Institut","host_organization_lineage":["https://openalex.org/I4210148506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1812.04889","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.04889","pdf_url":"https://arxiv.org/pdf/1812.04889","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W24460554","https://openalex.org/W209576205","https://openalex.org/W1668437634","https://openalex.org/W1965104497","https://openalex.org/W1973212083","https://openalex.org/W2005632248","https://openalex.org/W2008008473","https://openalex.org/W2060076025","https://openalex.org/W2062861068","https://openalex.org/W2092168430","https://openalex.org/W2104800030","https://openalex.org/W2150879147","https://openalex.org/W2160623568","https://openalex.org/W2579711798","https://openalex.org/W2592623476","https://openalex.org/W2777817795","https://openalex.org/W2893822386","https://openalex.org/W2962763863","https://openalex.org/W2962917950","https://openalex.org/W2963817075","https://openalex.org/W3109220575","https://openalex.org/W3149667697","https://openalex.org/W3204708751"],"related_works":["https://openalex.org/W3157378589","https://openalex.org/W3185579339","https://openalex.org/W3136591667","https://openalex.org/W1562672780","https://openalex.org/W2001533376","https://openalex.org/W2738400070","https://openalex.org/W2007826580","https://openalex.org/W3036444979","https://openalex.org/W2004744282","https://openalex.org/W2025631640","https://openalex.org/W3176426993","https://openalex.org/W1542720349","https://openalex.org/W3112559926","https://openalex.org/W2593847166","https://openalex.org/W174882013","https://openalex.org/W2803694591","https://openalex.org/W2000071030","https://openalex.org/W2118217932","https://openalex.org/W2358752394","https://openalex.org/W2949073205"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,30],"modification":[3,121],"of":[4,8,24,38,54,69,85,97],"the":[5,9,19,22,25,36,39,43,49,55,59,67,70,74,77,83,86,105,112,124,128,135,142,146],"Crouzeix--Raviart":[6],"discretization":[7],"Stokes":[10],"equations":[11],"in":[12,18,29,95],"arbitrary":[13],"dimension":[14],"which":[15],"is":[16,33,52,63,80,139],"quasi-optimal,":[17],"sense":[20],"that":[21],"error":[23,37,51,57,72],"discrete":[26,60],"velocity":[27,45,50,61,71,113],"field":[28,62],"broken":[31],"$H^1$-norm":[32],"proportional":[34,81,140],"to":[35,42,82,141],"best":[40,88],"approximation":[41],"analytical":[44],"field.":[46],"In":[47],"particular,":[48],"independent":[53],"pressure":[56,78,115],"and":[58,100,114],"elementwise":[64],"solenoidal.":[65],"Moreover,":[66],"sum":[68,84],"times":[73],"viscosity":[75],"plus":[76],"$L^2$-error":[79],"respective":[87],"errors.":[89],"All":[90],"proportionality":[91],"constants":[92],"are":[93],"bounded":[94],"terms":[96],"shape":[98],"regularity":[99],"do":[101],"not":[102],"depend":[103],"on":[104],"viscosity.":[106],"For":[107],"simply":[108],"connected":[109],"two-dimensional":[110],"domains,":[111],"can":[116],"be":[117],"computed":[118],"separately.":[119],"The":[120,131],"only":[122],"affects":[123],"right-hand":[125],"side,":[126],"aka":[127],"load":[129,137,148],"vector.":[130,149],"cost":[132,143],"for":[133,144],"building":[134,145],"modified":[136],"vector":[138],"standard":[147],"Some":[150],"numerical":[151],"experiments":[152],"illustrate":[153],"our":[154],"theoretical":[155],"results.":[156]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
