{"id":"https://openalex.org/W2016966935","doi":"https://doi.org/10.1137/s003614290037589x","title":"Superconvergence of Finite Element Approximations for the Stokes Problem by Projection Methods","display_name":"Superconvergence of Finite Element Approximations for the Stokes Problem by Projection Methods","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2016966935","doi":"https://doi.org/10.1137/s003614290037589x","mag":"2016966935"},"language":"en","primary_location":{"id":"doi:10.1137/s003614290037589x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290037589x","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/A5102719455","display_name":"Junping Wang","orcid":"https://orcid.org/0009-0005-6813-4499"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Junping Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032062029","display_name":"Xiu Ye","orcid":"https://orcid.org/0000-0002-1559-3836"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiu Ye","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102719455"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5309,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.81082243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"3","first_page":"1001","last_page":"1013"},"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":0.9983999729156494,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983000159263611,"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/superconvergence","display_name":"Superconvergence","score":0.9773714542388916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8645418882369995},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.822466254234314},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7787160277366638},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6344234347343445},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5793750286102295},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5289860963821411},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5152797698974609},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5105081796646118},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4873989224433899},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.47122514247894287},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42388927936553955},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4232668876647949},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17790398001670837},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10256204009056091},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.09444841742515564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05516591668128967}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9773714542388916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8645418882369995},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.822466254234314},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7787160277366638},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6344234347343445},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5793750286102295},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5289860963821411},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5152797698974609},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5105081796646118},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4873989224433899},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.47122514247894287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42388927936553955},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4232668876647949},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17790398001670837},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10256204009056091},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.09444841742515564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05516591668128967},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s003614290037589x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290037589x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1980964769","https://openalex.org/W1988234876","https://openalex.org/W2005601391","https://openalex.org/W2010332082","https://openalex.org/W2044892973","https://openalex.org/W2062002217","https://openalex.org/W2066748245","https://openalex.org/W2080246801","https://openalex.org/W2150140956","https://openalex.org/W2331941476","https://openalex.org/W4230989996","https://openalex.org/W4232913712"],"related_works":["https://openalex.org/W2019032602","https://openalex.org/W3199641408","https://openalex.org/W1992075486","https://openalex.org/W3138649314","https://openalex.org/W2947552135","https://openalex.org/W2014920306","https://openalex.org/W2984453791","https://openalex.org/W1982175859","https://openalex.org/W2788781272","https://openalex.org/W2046881738"],"abstract_inverted_index":{"This":[0],"paper":[1],"derives":[2],"a":[3,69],"general":[4],"superconvergence":[5,38],"result":[6,39],"for":[7,32,46,72],"finite":[8,55,74],"element":[9,56,75],"approximations":[10],"of":[11,86],"the":[12,33,47,81],"Stokes":[13,48],"problem":[14,49],"by":[15,23],"using":[16],"projection":[17],"methods":[18],"proposed":[19],"and":[20,50,88],"analyzed":[21],"recently":[22],"Wang":[24],"[J.":[25],"Math.":[26],"Study,":[27],"33":[28],"(2000),":[29],"pp.":[30],"229--243]":[31],"standard":[34],"Galerkin":[35],"method.":[36],"The":[37,63],"is":[40,51,65],"based":[41],"on":[42],"some":[43],"regularity":[44],"assumption":[45],"applicable":[52],"to":[53,67,79],"any":[54],"method":[57,64],"with":[58],"regular":[59],"but":[60],"nonuniform":[61],"partitions.":[62],"proved":[66],"give":[68],"convergent":[70],"scheme":[71],"certain":[73],"spaces":[76],"which":[77],"fail":[78],"satisfy":[80],"well-known":[82],"uniform":[83],"inf-sup":[84],"condition":[85],"Brezzi":[87],"Babuska.":[89]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
