{"id":"https://openalex.org/W2086256304","doi":"https://doi.org/10.1090/s0025-5718-08-02177-7","title":"An error estimate for two-dimensional Stokes driven cavity flow","display_name":"An error estimate for two-dimensional Stokes driven cavity flow","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W2086256304","doi":"https://doi.org/10.1090/s0025-5718-08-02177-7","mag":"2086256304"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02177-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02177-7","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, Indiana 47907","Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, Indiana 47907","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100659878","display_name":"Yanqiu Wang","orcid":"https://orcid.org/0000-0003-4783-1920"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yanqiu Wang","raw_affiliation_strings":["Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078","Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma , 74078"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078","institution_ids":["https://openalex.org/I115475287"]},{"raw_affiliation_string":"Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma , 74078","institution_ids":["https://openalex.org/I115475287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023481731"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":0.7636,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.74892258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"78","issue":"266","first_page":"771","last_page":"787"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.7811892032623291},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.6740865111351013},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6126496195793152},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5641108751296997},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5588017702102661},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.534939706325531},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.46890202164649963},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.45800280570983887},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3152400553226471},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20266687870025635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7811892032623291},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.6740865111351013},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6126496195793152},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5641108751296997},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5588017702102661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.534939706325531},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.46890202164649963},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.45800280570983887},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3152400553226471},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20266687870025635},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-08-02177-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02177-7","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.7129","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.7129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/0000-000-00/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.8330","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.8330","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.572.2992","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.572.2992","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.math.okstate.edu/~yqwang/publications/stokeserror.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02177-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02177-7","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02177-7/S0025-5718-08-02177-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2086256304.pdf","grobid_xml":"https://content.openalex.org/works/W2086256304.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W125509687","https://openalex.org/W136185420","https://openalex.org/W202544164","https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1674659126","https://openalex.org/W1775501378","https://openalex.org/W1852082788","https://openalex.org/W1969838226","https://openalex.org/W1983819408","https://openalex.org/W2003491112","https://openalex.org/W2006617763","https://openalex.org/W2014744421","https://openalex.org/W2021767118","https://openalex.org/W2026991963","https://openalex.org/W2037788590","https://openalex.org/W2041523977","https://openalex.org/W2044975742","https://openalex.org/W2077186677","https://openalex.org/W2097427900","https://openalex.org/W2133248904","https://openalex.org/W2592623476","https://openalex.org/W3149667697","https://openalex.org/W4252104256","https://openalex.org/W4292166829","https://openalex.org/W6826525772"],"related_works":["https://openalex.org/W2055836843","https://openalex.org/W2755775996","https://openalex.org/W2773728674","https://openalex.org/W2069701013","https://openalex.org/W2366062865","https://openalex.org/W2095941963","https://openalex.org/W2760505775","https://openalex.org/W2011633066","https://openalex.org/W4200392369","https://openalex.org/W2111215486"],"abstract_inverted_index":{"Discontinuous":[0],"velocity":[1,39],"boundary":[2,143],"data":[3],"for":[4,29,150],"the":[5,26,30,38,142,152,156,160],"lid":[6],"driven":[7,31,163],"cavity":[8,32,164],"flow":[9,33],"has":[10],"long":[11],"been":[12],"causing":[13],"difficulties":[14],"in":[15,42],"both":[16,151],"theoretical":[17],"analysis":[18],"and":[19,136,155],"numerical":[20],"simulations.":[21],"In":[22],"finite":[23],"element":[24],"methods,":[25],"variational":[27],"form":[28],"is":[34,40],"not":[35,41,70],"valid":[36],"since":[37],"<inline-formula":[43,75,106],"content-type=\"math/mathml\">":[44,76,107],"<mml:math":[45,77,108],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[46,78,109],"alttext=\"bold-italic":[47],"upper":[48,80],"H":[49],"Superscript":[50,82],"1\">":[51],"<mml:semantics>":[52,86,117],"<mml:msup>":[53,87],"<mml:mi":[54,90],"mathvariant=\"bold-italic\">H</mml:mi>":[55],"<mml:mn>1</mml:mn>":[56,95,121],"</mml:msup>":[57,99],"<mml:annotation":[58,100,129],"encoding=\"application/x-tex\">\\boldsymbol":[59],"{H}^1</mml:annotation>":[60],"</mml:semantics>":[61,103,132],"</mml:math>":[62,104,133],"</inline-formula>":[63,105,134],".":[64],"Hence":[65],"standard":[66],"error":[67,148],"estimates":[68,149],"do":[69],"work.":[71],"By":[72],"using":[73],"only":[74],"alttext=\"bold":[79],"W":[81],"1":[83,111],"comma":[84],"r\">":[85],"<mml:mrow":[88,93],"class=\"MJX-TeXAtom-ORD\">":[89,94],"mathvariant=\"bold\">W</mml:mi>":[91],"</mml:mrow>":[92,98,128],"<mml:mo>,</mml:mo>":[96],"<mml:mi>r</mml:mi>":[97,123],"encoding=\"application/x-tex\">\\mathbf":[101],"{W}^{1,r}</mml:annotation>":[102],"alttext=\"left-parenthesis":[110],"greater-than":[112,114],"r":[113],"2":[115],"right-parenthesis\">":[116],"<mml:mrow>":[118],"<mml:mo":[119,126],"stretchy=\"false\">(</mml:mo>":[120],"<mml:mo>&gt;</mml:mo>":[122,124],"<mml:mn>2</mml:mn>":[125],"stretchy=\"false\">)</mml:mo>":[127],"encoding=\"application/x-tex\">(1&gt;r&gt;":[130],"2)</mml:annotation>":[131],"regularity":[135],"constructing":[137],"a":[138],"continuous":[139],"approximation":[140],"to":[141],"data,":[144],"here":[145],"we":[146],"present":[147],"velocity-pressure":[153],"formulation":[154,158],"pseudostress-velocity":[157],"of":[159],"two-dimensional":[161],"Stokes":[162],"flow.":[165]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}