{"id":"https://openalex.org/W2169575140","doi":"https://doi.org/10.1137/s1064827502407718","title":"A Taxonomy of Consistently Stabilized Finite Element Methods for the Stokes Problem","display_name":"A Taxonomy of Consistently Stabilized Finite Element Methods for the Stokes Problem","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2169575140","doi":"https://doi.org/10.1137/s1064827502407718","mag":"2169575140"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502407718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502407718","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5037326863","display_name":"Teri Barth","orcid":null},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Teri Barth","raw_affiliation_strings":["Computational Mathematics and Algorithms Department, Sandia National Laboratories, Albu-querque, NM 87185-1110"],"affiliations":[{"raw_affiliation_string":"Computational Mathematics and Algorithms Department, Sandia National Laboratories, Albu-querque, NM 87185-1110","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022276974","display_name":"Pavel Bochev","orcid":"https://orcid.org/0000-0002-8721-7119"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pavel Bochev","raw_affiliation_strings":["Computational Mathematics and Algorithms Department, Sandia National Laboratories, Albu-querque, NM 87185-1110"],"affiliations":[{"raw_affiliation_string":"Computational Mathematics and Algorithms Department, Sandia National Laboratories, Albu-querque, NM 87185-1110","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max Gunzburger","raw_affiliation_strings":["School of Computational Science and Information Technology, Florida State University, Talla-hassee, FL 32306-4120"],"affiliations":[{"raw_affiliation_string":"School of Computational Science and Information Technology, Florida State University, Talla-hassee, FL 32306-4120","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018004800","display_name":"John N. Shadid","orcid":"https://orcid.org/0009-0001-9804-1649"},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Shadid","raw_affiliation_strings":["Computational Sciences Department, Sandia National Laboratories, Albuquerque, NM 87185"],"affiliations":[{"raw_affiliation_string":"Computational Sciences Department, Sandia National Laboratories, Albuquerque, NM 87185","institution_ids":["https://openalex.org/I4210104735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037326863"],"corresponding_institution_ids":["https://openalex.org/I192454743"],"apc_list":null,"apc_paid":null,"fwci":8.191,"has_fulltext":false,"cited_by_count":95,"citation_normalized_percentile":{"value":0.98118603,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"25","issue":"5","first_page":"1585","last_page":"1607"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8216314911842346},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6718093752861023},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6615486741065979},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.6191340088844299},{"id":"https://openalex.org/keywords/coercivity","display_name":"Coercivity","score":0.5399870872497559},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5200231075286865},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.495234876871109},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.48312684893608093},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.44859588146209717},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43416187167167664},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42061495780944824},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3366551399230957},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3112943768501282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2927801012992859},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10244077444076538}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216314911842346},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6718093752861023},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6615486741065979},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.6191340088844299},{"id":"https://openalex.org/C126530901","wikidata":"https://www.wikidata.org/wiki/Q432635","display_name":"Coercivity","level":2,"score":0.5399870872497559},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5200231075286865},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.495234876871109},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.48312684893608093},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.44859588146209717},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43416187167167664},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42061495780944824},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3366551399230957},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3112943768501282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2927801012992859},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10244077444076538},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","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/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/s1064827502407718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502407718","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.333.2869","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.2869","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.sc.fsu.edu/~mgunzburger/files_papers/gunzburger-stab1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.799.6452","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.799.6452","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.sandia.gov/%7Epbboche/papers_pdf/2004SISC_Tax.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1741288133","display_name":null,"funder_award_id":"Sandia","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G3821936529","display_name":null,"funder_award_id":"Sandia","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7340972926","display_name":null,"funder_award_id":"other","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W653136046","https://openalex.org/W1488435683","https://openalex.org/W1506342804","https://openalex.org/W1560263223","https://openalex.org/W1674659126","https://openalex.org/W1708679080","https://openalex.org/W1986608219","https://openalex.org/W1992896789","https://openalex.org/W1998338423","https://openalex.org/W2024621437","https://openalex.org/W2034150466","https://openalex.org/W2039259138","https://openalex.org/W2041523977","https://openalex.org/W2049707725","https://openalex.org/W2056399160","https://openalex.org/W2065438814","https://openalex.org/W2068845153","https://openalex.org/W2070236116","https://openalex.org/W2081177856","https://openalex.org/W2085259167","https://openalex.org/W2101196233","https://openalex.org/W2140153041","https://openalex.org/W2289366489","https://openalex.org/W2328632875","https://openalex.org/W2596951540","https://openalex.org/W2934526567","https://openalex.org/W2994660742","https://openalex.org/W4205624883","https://openalex.org/W4205634890","https://openalex.org/W4251180451","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W4232597038","https://openalex.org/W4229076095","https://openalex.org/W1984631837","https://openalex.org/W2787172707","https://openalex.org/W2154704909","https://openalex.org/W2101857978","https://openalex.org/W2071928229","https://openalex.org/W2597066370","https://openalex.org/W2388312018","https://openalex.org/W2031334333"],"abstract_inverted_index":{"Abstract.":[0],"Stabilized":[1],"mixed":[2],"methods":[3,20,85,129],"can":[4],"circumvent":[5],"the":[6,141,145],"restrictive":[7],"inf-sup":[8],"condition":[9],"without":[10],"introducing":[11],"penalty":[12],"errors.":[13],"For":[14],"properly":[15],"chosen":[16],"stabilization":[17,37],"parameters":[18],"these":[19,80],"are":[21,117],"well-posed":[22],"for":[23,104,123],"all":[24],"conforming":[25],"velocity-pressure":[26],"pairs.":[27],"However,":[28],"their":[29,87],"variational":[30],"forms":[31,47],"have":[32],"widely":[33],"varying":[34],"properties.":[35,61],"First,":[36],"offers":[38],"a":[39,68,72,98],"choice":[40,70],"between":[41],"weakly":[42],"or":[43],"strongly":[44,105],"coercive":[45,106],"bilinear":[46],"that":[48,96,144],"give":[49],"rise":[50],"to":[51],"linear":[52],"systems":[53],"with":[54,119,135],"identical":[55],"solutions":[56],"but":[57],"very":[58],"different":[59],"matrix":[60],"Second,":[62],"coercivity":[63],"may":[64],"be":[65],"conditional":[66],"upon":[67],"proper":[69],"of":[71,83,100,127],"stabilizing":[73],"parameter.":[74],"Here":[75],"we":[76],"focus":[77],"on":[78],"how":[79],"two":[81,124],"aspects":[82],"stabilized":[84,128,147],"affect":[86],"accuracy":[88],"and":[89,114],"efficient":[90],"iterative":[91],"solution.":[92],"We":[93],"present":[94],"results":[95],"indicate":[97,140],"preference":[99],"Krylov":[101],"subspace":[102],"solvers":[103],"formulations.":[107],"Stability":[108],"criteria":[109],"obtained":[110],"by":[111],"finite":[112],"element":[113],"algebraic":[115],"analyses":[116],"compared":[118],"numerical":[120,136],"experiments.":[121],"While":[122],"popular":[125],"classes":[126],"sufficient":[130],"stability":[131],"bounds":[132],"correlate":[133],"well":[134],"stability,":[137],"our":[138],"experiments":[139],"intriguing":[142],"possibility":[143],"pressure":[146],"Galerkin":[148],"method":[149],"is":[150],"unconditionally":[151],"stable.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
