{"id":"https://openalex.org/W1973590664","doi":"https://doi.org/10.1137/050623176","title":"Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem","display_name":"Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1973590664","doi":"https://doi.org/10.1137/050623176","mag":"1973590664"},"language":"en","primary_location":{"id":"doi:10.1137/050623176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050623176","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":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3228708","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001469709","display_name":"Rodolfo Araya","orcid":"https://orcid.org/0000-0002-1165-3969"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Rodolfo Araya","raw_affiliation_strings":["Universidad de Concepcion#TAB#"],"affiliations":[{"raw_affiliation_string":"Universidad de Concepcion#TAB#","institution_ids":["https://openalex.org/I172787465"]}]},{"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/A5059362886","display_name":"Fr\u00e9d\u00e9ric Valentin","orcid":"https://orcid.org/0000-0002-5056-7529"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Valentin","raw_affiliation_strings":["Universidad de Concepcion#TAB#"],"affiliations":[{"raw_affiliation_string":"Universidad de Concepcion#TAB#","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001469709"],"corresponding_institution_ids":["https://openalex.org/I172787465"],"apc_list":null,"apc_paid":null,"fwci":6.4041,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.96945316,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"44","issue":"1","first_page":"322","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"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/T11558","display_name":"Composite Material Mechanics","score":0.9988999962806702,"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/piecewise","display_name":"Piecewise","score":0.8479723334312439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8201612234115601},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6878697872161865},{"id":"https://openalex.org/keywords/constant-function","display_name":"Constant function","score":0.5899096727371216},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5855875015258789},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5732669234275818},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5673753619194031},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5621055960655212},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5609665513038635},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4865233302116394},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4803932309150696},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.4705265760421753},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46974021196365356},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.464804083108902},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.44454097747802734},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43247556686401367},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43191269040107727},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.410381942987442},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.36260920763015747},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.08803033828735352},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.07756263017654419}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8479723334312439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8201612234115601},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6878697872161865},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.5899096727371216},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5855875015258789},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5732669234275818},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5673753619194031},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5621055960655212},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5609665513038635},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4865233302116394},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4803932309150696},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.4705265760421753},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46974021196365356},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.464804083108902},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.44454097747802734},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43247556686401367},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43191269040107727},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.410381942987442},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.36260920763015747},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.08803033828735352},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.07756263017654419},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":7,"locations":[{"id":"doi:10.1137/050623176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050623176","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:4883","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/566211.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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.540.9562","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.540.9562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lncc.br/~valentin/docs/AraBarVal06.pdf","raw_type":"text"},{"id":"pmh:oai:americanae.aecid.es:3228708","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3228708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:americanae.aecid.es:3228709","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3228709","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/177171","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/177171","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/177172","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/177172","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3228708","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3228708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W124532162","https://openalex.org/W1515623627","https://openalex.org/W1585098889","https://openalex.org/W1601728065","https://openalex.org/W1674659126","https://openalex.org/W1966480196","https://openalex.org/W1974006019","https://openalex.org/W1976509668","https://openalex.org/W1977399978","https://openalex.org/W1986608219","https://openalex.org/W1987031962","https://openalex.org/W1994851625","https://openalex.org/W2011078493","https://openalex.org/W2011185352","https://openalex.org/W2020275136","https://openalex.org/W2029918260","https://openalex.org/W2041589227","https://openalex.org/W2043882304","https://openalex.org/W2053342859","https://openalex.org/W2056399160","https://openalex.org/W2067208724","https://openalex.org/W2070236116","https://openalex.org/W2074772185","https://openalex.org/W2079925282","https://openalex.org/W2081177856","https://openalex.org/W2082621526","https://openalex.org/W2095399846","https://openalex.org/W2126715817","https://openalex.org/W2155879256","https://openalex.org/W2169575140","https://openalex.org/W2266970012","https://openalex.org/W2289366489","https://openalex.org/W2625528991","https://openalex.org/W4236548481","https://openalex.org/W4242273588","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W2376732695","https://openalex.org/W1989473560","https://openalex.org/W2565231037","https://openalex.org/W1977906733","https://openalex.org/W1567939749","https://openalex.org/W2185206193","https://openalex.org/W2100864966","https://openalex.org/W1979202874","https://openalex.org/W3196813885","https://openalex.org/W1992855575"],"abstract_inverted_index":{"This":[0],"work":[1],"concerns":[2],"the":[3,11,30,33,38,49,53,57,106],"development":[4],"of":[5,20,32],"stabilized":[6],"finite":[7],"element":[8,50],"methods":[9],"for":[10,37,81,90],"Stokes":[12],"problem":[13],"considering":[14],"nonstable":[15],"different":[16],"(or":[17],"equal)":[18],"order":[19,97],"velocity":[21,39,86],"and":[22,87,89,102],"pressure":[23,88],"interpolations.":[24],"The":[25],"approach":[26,68],"is":[27,61,69],"based":[28],"on":[29,48],"enrichment":[31],"standard":[34],"polynomial":[35],"space":[36,60],"component":[40],"with":[41,63],"multiscale":[42],"functions":[43],"which":[44],"no":[45],"longer":[46],"vanish":[47],"boundary.":[51],"On":[52],"other":[54],"hand,":[55],"since":[56],"test":[58],"function":[59],"enriched":[62],"bubble-like":[64],"functions,":[65],"a":[66,74],"Petrov--Galerkin":[67],"employed.":[70],"We":[71],"use":[72],"such":[73],"strategy":[75],"to":[76],"propose":[77],"stable":[78],"variational":[79],"formulations":[80],"continuous":[82],"piecewise":[83,91],"linear":[84],"in":[85],"linear/piecewise":[92],"constant":[93],"interpolation":[94],"pairs.":[95],"Optimal":[96],"convergence":[98],"results":[99],"are":[100],"derived":[101],"numerical":[103],"tests":[104],"validate":[105],"proposed":[107],"methods.":[108]},"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":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}