{"id":"https://openalex.org/W3164465204","doi":"https://doi.org/10.1515/jnma-2021-0125","title":"A divergence-free finite element method for the Stokes problem with boundary correction","display_name":"A divergence-free finite element method for the Stokes problem with boundary correction","publication_year":2022,"publication_date":"2022-04-14","ids":{"openalex":"https://openalex.org/W3164465204","doi":"https://doi.org/10.1515/jnma-2021-0125","mag":"3164465204"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2021-0125","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0125","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5100449219","display_name":"Haoran Liu","orcid":"https://orcid.org/0000-0001-7754-9454"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Haoran Liu","raw_affiliation_strings":["Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039552338","display_name":"Michael Neilan","orcid":"https://orcid.org/0000-0002-1564-1041"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Neilan","raw_affiliation_strings":["Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089504569","display_name":"M. Baris Otus","orcid":null},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Baris Otus","raw_affiliation_strings":["Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Pittsburgh , Pittsburgh , PA 15260 , USA","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170201317"],"apc_list":null,"apc_paid":null,"fwci":0.6349,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57373558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"31","issue":"2","first_page":"105","last_page":"123"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9979000091552734,"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":0.8798689246177673},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.8768655061721802},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7400848269462585},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6156442761421204},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5916833877563477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5892725586891174},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5541498064994812},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5186464190483093},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.4925549626350403},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4881308972835541},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4630216956138611},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.15759006142616272},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.146551251411438}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8798689246177673},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8768655061721802},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7400848269462585},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6156442761421204},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5916833877563477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5892725586891174},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5541498064994812},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5186464190483093},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.4925549626350403},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4881308972835541},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4630216956138611},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.15759006142616272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.146551251411438},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2021-0125","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0125","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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":41,"referenced_works":["https://openalex.org/W140909251","https://openalex.org/W1866311589","https://openalex.org/W1964923523","https://openalex.org/W1973212083","https://openalex.org/W1988228958","https://openalex.org/W1993455955","https://openalex.org/W1997972083","https://openalex.org/W2005632248","https://openalex.org/W2017319812","https://openalex.org/W2040567494","https://openalex.org/W2049902336","https://openalex.org/W2058241749","https://openalex.org/W2075330220","https://openalex.org/W2079423956","https://openalex.org/W2122379318","https://openalex.org/W2164454265","https://openalex.org/W2319306682","https://openalex.org/W2410416051","https://openalex.org/W2618791333","https://openalex.org/W2744050773","https://openalex.org/W2754767899","https://openalex.org/W2767049640","https://openalex.org/W2893959109","https://openalex.org/W2962917950","https://openalex.org/W2963005283","https://openalex.org/W2964135693","https://openalex.org/W2971574404","https://openalex.org/W2974425401","https://openalex.org/W2994986471","https://openalex.org/W3000142798","https://openalex.org/W3008730422","https://openalex.org/W3032567946","https://openalex.org/W3080938804","https://openalex.org/W3091675879","https://openalex.org/W3100556510","https://openalex.org/W3102533448","https://openalex.org/W3134671735","https://openalex.org/W3158636760","https://openalex.org/W3204708751","https://openalex.org/W4233665781","https://openalex.org/W4233895458"],"related_works":["https://openalex.org/W2081441772","https://openalex.org/W4245322218","https://openalex.org/W2074195844","https://openalex.org/W4210327724","https://openalex.org/W2052109794","https://openalex.org/W2089246697","https://openalex.org/W2951836888","https://openalex.org/W2074759558","https://openalex.org/W3164465204","https://openalex.org/W4302066665"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"constructs":[3],"and":[4,36,75,105],"analyzes":[5],"a":[6],"boundary":[7,67,73],"correction":[8],"finite":[9],"element":[10],"method":[11,100],"for":[12],"the":[13,18,37,66,78,89,92,99,106],"Stokes":[14],"problem":[15],"based":[16],"on":[17,21],"Scott\u2013Vogelius":[19],"pair":[20],"Clough\u2013Tocher":[22],"splits.":[23],"The":[24],"velocity":[25,107],"space":[26,39,56],"consists":[27,40,58],"of":[28,32,41,44,59,80,91],"continuous":[29,60],"piecewise":[30,42,61],"polynomials":[31,43,62],"degree":[33,45],"k":[34,47],",":[35],"pressure":[38],"(":[46],"\u2013":[48],"1)":[49],"without":[50],"continuity":[51],"constraints.":[52],"A":[53],"Lagrange":[54],"multiplier":[55],"that":[57,98],"with":[63,102],"respect":[64],"to":[65,71,76,88],"partition":[68],"is":[69,109],"introduced":[70],"enforce":[72],"conditions":[74],"mitigate":[77],"lack":[79],"pressure-robustness.":[81],"We":[82],"prove":[83],"several":[84],"inf-sup":[85],"conditions,":[86],"leading":[87],"well-posedness":[90],"method.":[93],"In":[94],"addition,":[95],"we":[96],"show":[97],"converges":[101],"optimal":[103],"order":[104],"approximation":[108],"divergence-free.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}