{"id":"https://openalex.org/W2038848585","doi":"https://doi.org/10.1137/090771508","title":"A Posteriori Error Estimates of Stabilization of Low-Order Mixed Finite Elements for Incompressible Flow","display_name":"A Posteriori Error Estimates of Stabilization of Low-Order Mixed Finite Elements for Incompressible Flow","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2038848585","doi":"https://doi.org/10.1137/090771508","mag":"2038848585"},"language":"en","primary_location":{"id":"doi:10.1137/090771508","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771508","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/A5039484634","display_name":"Haibiao Zheng","orcid":"https://orcid.org/0000-0003-3910-7174"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haibiao Zheng","raw_affiliation_strings":["hbzheng13@gmail.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hbzheng13@gmail.com#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108057376","display_name":"Yanren Hou","orcid":"https://orcid.org/0000-0002-3425-0433"},"institutions":[{"id":"https://openalex.org/I1325784139","display_name":"Yahoo (United Kingdom)","ror":"https://ror.org/038p3gq39","country_code":"GB","type":"company","lineage":["https://openalex.org/I1325784139","https://openalex.org/I4210134091"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yanren Hou","raw_affiliation_strings":["yrhou@mail.xjtu.edu.cn and fengshi81@yahoo.com.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"yrhou@mail.xjtu.edu.cn and fengshi81@yahoo.com.cn#TAB#","institution_ids":["https://openalex.org/I1325784139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057783778","display_name":"F. Shi","orcid":"https://orcid.org/0000-0002-7491-5188"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng Shi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0984,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9144815,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"32","issue":"3","first_page":"1346","last_page":"1360"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9986000061035156,"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/estimator","display_name":"Estimator","score":0.8707141876220703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.848212718963623},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7081903219223022},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6842961311340332},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6659103631973267},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5927948355674744},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5360944867134094},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.4447517693042755},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4111383557319641},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35778379440307617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29842206835746765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1655856966972351},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08690086007118225}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8707141876220703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.848212718963623},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7081903219223022},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6842961311340332},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6659103631973267},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5927948355674744},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5360944867134094},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.4447517693042755},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4111383557319641},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35778379440307617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29842206835746765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1655856966972351},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08690086007118225},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090771508","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771508","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1980659254","https://openalex.org/W1980964769","https://openalex.org/W1989594010","https://openalex.org/W1994336408","https://openalex.org/W1995404822","https://openalex.org/W1999807552","https://openalex.org/W2003049157","https://openalex.org/W2044892973","https://openalex.org/W2045382809","https://openalex.org/W2049914863","https://openalex.org/W2050178911","https://openalex.org/W2063899632","https://openalex.org/W2066927514","https://openalex.org/W2071036364","https://openalex.org/W2076074132","https://openalex.org/W2079227383","https://openalex.org/W2090899749","https://openalex.org/W2091775502","https://openalex.org/W2119859226","https://openalex.org/W2122602456","https://openalex.org/W2155395549","https://openalex.org/W2163694039","https://openalex.org/W2381246980","https://openalex.org/W2934526567","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1507702947","https://openalex.org/W2022062253"],"abstract_inverted_index":{"In":[0,52],"this":[1],"paper,":[2],"we":[3,27],"derive":[4],"a":[5],"posteriori":[6],"error":[7,46,56],"estimates":[8],"for":[9,18],"the":[10,19,36,45,64,72,87],"stabilization":[11],"of":[12,47],"low-order":[13],"mixed":[14],"finite":[15,49],"element":[16,50],"methods":[17],"Stokes":[20],"equations.":[21],"By":[22],"defining":[23],"different":[24],"projection":[25,78],"estimators,":[26],"prove":[28],"that,":[29],"up":[30],"to":[31,60,63,82],"higher":[32],"order":[33],"perturbation":[34],"terms,":[35],"estimators":[37,79],"yield":[38],"global":[39],"upper":[40],"and":[41],"lower":[42],"bounds":[43],"on":[44,76],"stabilized":[48],"methods.":[51],"numerical":[53],"tests,":[54],"each":[55],"estimator":[57],"is":[58,68,80],"shown":[59,70],"be":[61],"equivalent":[62],"discretization":[65],"error.":[66],"It":[67],"also":[69],"that":[71],"adaptive":[73],"strategy":[74],"based":[75],"both":[77],"efficient":[81],"detect":[83],"local":[84],"singularities":[85],"in":[86],"flow":[88],"problems.":[89]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
