{"id":"https://openalex.org/W2612288776","doi":"https://doi.org/10.1137/15m1050550","title":"Stability and Superconvergence of MAC Scheme for Stokes Equations on Nonuniform Grids","display_name":"Stability and Superconvergence of MAC Scheme for Stokes Equations on Nonuniform Grids","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2612288776","doi":"https://doi.org/10.1137/15m1050550","mag":"2612288776"},"language":"en","primary_location":{"id":"doi:10.1137/15m1050550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1050550","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/A5026218668","display_name":"Hongxing Rui","orcid":"https://orcid.org/0000-0003-2166-2321"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hongxing Rui","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100418681","display_name":"Xiaoli Li","orcid":"https://orcid.org/0000-0002-3885-7099"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoli Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026218668"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4332,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.94841789,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"55","issue":"3","first_page":"1135","last_page":"1158"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.9931390285491943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8211495876312256},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6447276473045349},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6369465589523315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5163315534591675},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4833326041698456},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4513295888900757},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.44092506170272827},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.40393948554992676},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3559810519218445},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.10172876715660095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08964276313781738},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07183516025543213}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9931390285491943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8211495876312256},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6447276473045349},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6369465589523315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5163315534591675},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4833326041698456},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4513295888900757},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.44092506170272827},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.40393948554992676},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3559810519218445},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.10172876715660095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08964276313781738},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07183516025543213},{"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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1050550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1050550","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":[{"id":"https://openalex.org/G289046561","display_name":null,"funder_award_id":"11671233","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3058161258","display_name":null,"funder_award_id":"91330106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1504595764","https://openalex.org/W1974112851","https://openalex.org/W1998788695","https://openalex.org/W1999559145","https://openalex.org/W2001877072","https://openalex.org/W2005293667","https://openalex.org/W2007628212","https://openalex.org/W2013029478","https://openalex.org/W2014339952","https://openalex.org/W2015975209","https://openalex.org/W2024054122","https://openalex.org/W2030563293","https://openalex.org/W2031733801","https://openalex.org/W2034426212","https://openalex.org/W2041211945","https://openalex.org/W2076333918","https://openalex.org/W2077045211","https://openalex.org/W2078133941","https://openalex.org/W2086818669","https://openalex.org/W2094779668","https://openalex.org/W2126431081","https://openalex.org/W2142654352","https://openalex.org/W2147446841","https://openalex.org/W2157822890","https://openalex.org/W2161229398","https://openalex.org/W2327371110"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W2160252404","https://openalex.org/W4230524683","https://openalex.org/W2949279852","https://openalex.org/W1981510480","https://openalex.org/W2231544277","https://openalex.org/W4388482258"],"abstract_inverted_index":{"The":[0],"marker":[1],"and":[2,22,31,53,59,82,85,102,125],"cell":[3],"(MAC)":[4],"method,":[5],"a":[6],"class":[7],"of":[8,19,65,118,122,129,157],"finite":[9],"volume":[10],"schemes":[11,26],"based":[12],"on":[13,37,69,79,137],"staggered":[14],"grids,":[15],"has":[16,40],"been":[17,41],"one":[18],"the":[20,29,50,54,62,80,87,91,96,105,111,119,123,126,130,152,158],"simplest":[21],"most":[23],"effective":[24],"numerical":[25,35,159],"for":[27,56,61,99,104,115],"solving":[28],"Stokes":[30,67],"Navier--Stokes":[32],"equations.":[33],"Its":[34],"superconvergence":[36,94,114],"uniform":[38,138],"grids":[39],"observed":[42],"since":[43],"1992.":[44],"In":[45],"this":[46],"paper":[47],"we":[48,73],"establish":[49],"LBB":[51],"condition":[52],"stability":[55],"both":[57,100],"velocity":[58,81,101],"pressure":[60,103],"MAC":[63,106,153],"scheme":[64,154],"stationary":[66],"equations":[68],"nonuniform":[70],"grids.":[71,139],"Then":[72],"construct":[74],"an":[75],"auxiliary":[76],"function":[77],"depending":[78],"discretizing":[83],"parameters":[84],"analyze":[86],"superconvengence.":[88],"We":[89,108],"obtain":[90,110],"second":[92,112,134],"order":[93,113,135],"in":[95],"L2":[97],"norm":[98,121,132],"scheme.":[107],"also":[109],"some":[116],"terms":[117,128],"H1":[120,131],"velocity,":[124],"other":[127],"are":[133],"superconvergent":[136],"Our":[140],"analysis":[141],"can":[142],"be":[143],"extended":[144],"to":[145],"three":[146],"dimensional":[147],"problems.":[148],"Numerical":[149],"experiments":[150],"using":[151],"show":[155],"agreement":[156],"results":[160],"with":[161],"theoretical":[162],"analysis.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}