{"id":"https://openalex.org/W2077018328","doi":"https://doi.org/10.1137/140972755","title":"Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow","display_name":"Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2077018328","doi":"https://doi.org/10.1137/140972755","mag":"2077018328"},"language":"en","primary_location":{"id":"doi:10.1137/140972755","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140972755","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/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025324947","display_name":"Gabriel R. Barrenechea","orcid":"https://orcid.org/0000-0003-4490-678X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriel R. Barrenechea","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000967177","display_name":"Andreas Wachtel","orcid":"https://orcid.org/0000-0002-6317-787X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas Wachtel","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091196582"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.58515926,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80118394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"53","issue":"2","first_page":"1107","last_page":"1120"},"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":0.9986000061035156,"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":0.9962999820709229,"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/finite-element-method","display_name":"Finite element method","score":0.763492226600647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.748787522315979},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.728464663028717},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5606304407119751},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5557053089141846},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.525210440158844},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5223192572593689},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5193513631820679},{"id":"https://openalex.org/keywords/aspect-ratio","display_name":"Aspect ratio (aeronautics)","score":0.4825148284435272},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44208744168281555},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42266637086868286},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4175168573856354},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41446828842163086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3371990919113159},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2783069908618927},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.16040444374084473},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1429121494293213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09608203172683716}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.763492226600647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.748787522315979},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.728464663028717},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5606304407119751},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5557053089141846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.525210440158844},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5223192572593689},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5193513631820679},{"id":"https://openalex.org/C82558694","wikidata":"https://www.wikidata.org/wiki/Q1545619","display_name":"Aspect ratio (aeronautics)","level":2,"score":0.4825148284435272},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44208744168281555},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42266637086868286},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4175168573856354},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41446828842163086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3371990919113159},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2783069908618927},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.16040444374084473},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1429121494293213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09608203172683716},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140972755","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140972755","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:strathprints.strath.ac.uk:55338","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/137171.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1598074861","https://openalex.org/W1674659126","https://openalex.org/W1965880205","https://openalex.org/W1970446082","https://openalex.org/W1983131150","https://openalex.org/W1993101546","https://openalex.org/W1996764269","https://openalex.org/W2049332222","https://openalex.org/W2073341634","https://openalex.org/W2079286643","https://openalex.org/W2081327383","https://openalex.org/W2116825790","https://openalex.org/W2123500118"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W2237480245","https://openalex.org/W3134374554","https://openalex.org/W2519167559","https://openalex.org/W2075065631","https://openalex.org/W4288358396","https://openalex.org/W4311248832"],"abstract_inverted_index":{"Anisotropically":[0],"refined":[1],"mixed":[2,186],"finite":[3,147,157,187],"elements":[4,170],"are":[5,94,131],"beneficial":[6],"for":[7],"the":[8,18,21,28,32,38,59,65,76,84,88,99,103,118,122,127,138,142,155,165,169,181,185,191],"resolution":[9],"of":[10,20,31,46,61,87,121,144,168,180],"local":[11],"features":[12],"such":[13],"as":[14],"boundary":[15],"layers.":[16],"Unfortunately,":[17],"stability":[19,73,109],"resulting":[22],"scheme":[23,159,189],"is":[24,55,160],"highly":[25],"sensitive":[26],"to":[27,63,71,107,112,164,184],"aspect":[29,113,166],"ratio":[30,114,167],"elements.":[33],"Previous":[34],"analysis":[35],"revealed":[36],"that":[37,117,154,175],"degeneration":[39],"arises":[40],"from":[41],"a":[42,145],"relatively":[43],"small":[44],"number":[45],"spurious":[47,66],"(piecewise":[48],"constant)":[49],"pressure":[50,67,90,104,124,129],"modes.":[51],"The":[52,96],"present":[53],"article":[54],"concerned":[56],"with":[57,110,162],"resolving":[58],"problem":[60],"how":[62],"suppress":[64],"modes":[68],"in":[69,83],"order":[70],"restore":[72,108],"yet":[74],"at":[75],"same":[77,182],"time":[78],"not":[79],"incur":[80],"any":[81],"deterioration":[82],"approximation":[85,119,174],"properties":[86,120],"reduced":[89],"space.":[91,193],"Two":[92],"results":[93],"presented.":[95],"first":[97],"gives":[98],"minimal":[100],"constraints":[101],"on":[102],"space":[105,125,130],"needed":[106],"respect":[111,163],"and":[115,126,171],"shows":[116,153],"constrained":[123,192],"unconstrained":[128],"essentially":[132],"identical.":[133],"Alternatively,":[134],"one":[135],"can":[136],"impose":[137],"constraint":[139],"weakly":[140],"through":[141],"use":[143],"stabilized":[146,156],"element":[148,158,188],"scheme.":[149],"A":[150],"second":[151],"result":[152],"robust":[161],"produces":[172],"an":[173,177],"satisfies":[176],"error":[178],"bound":[179],"type":[183],"using":[190]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}