{"id":"https://openalex.org/W1996113663","doi":"https://doi.org/10.1137/050629008","title":"Convergence of Numerical Approximations of the Incompressible Navier\u2013Stokes Equations with Variable Density and Viscosity","display_name":"Convergence of Numerical Approximations of the Incompressible Navier\u2013Stokes Equations with Variable Density and Viscosity","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1996113663","doi":"https://doi.org/10.1137/050629008","mag":"1996113663"},"language":"en","primary_location":{"id":"doi:10.1137/050629008","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629008","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/A5003709575","display_name":"Chun Liu","orcid":"https://orcid.org/0000-0001-9319-1640"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chun Liu","raw_affiliation_strings":["Mathematics"],"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042222077","display_name":"Noel J. Walkington","orcid":"https://orcid.org/0000-0002-9128-0524"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Noel J. Walkington","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003709575"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8562,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.92495539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"3","first_page":"1287","last_page":"1304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9993000030517578,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9993000030517578,"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":0.9991999864578247,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.8533883094787598},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.5821307897567749},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5735505819320679},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5556235909461975},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.5539026260375977},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5336405038833618},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5177844762802124},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4823164939880371},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.48160478472709656},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.4513515532016754},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.44848358631134033},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4464277923107147},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41555094718933105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3476794362068176},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15382811427116394},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.14529219269752502},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.12779712677001953},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1277208924293518}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8533883094787598},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.5821307897567749},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5735505819320679},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5556235909461975},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.5539026260375977},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5336405038833618},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5177844762802124},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4823164939880371},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.48160478472709656},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.4513515532016754},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.44848358631134033},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4464277923107147},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41555094718933105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3476794362068176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15382811427116394},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.14529219269752502},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12779712677001953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1277208924293518},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050629008","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629008","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.208.4262","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.4262","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/CNA/Publications/publications2003/006abs/03-CNA-006.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1591043804","https://openalex.org/W1597209545","https://openalex.org/W1967167841","https://openalex.org/W1979413834","https://openalex.org/W1991113069","https://openalex.org/W1992812527","https://openalex.org/W2024343740","https://openalex.org/W2030119637","https://openalex.org/W2041523977","https://openalex.org/W2042226984","https://openalex.org/W2043876702","https://openalex.org/W2062389073","https://openalex.org/W2068039185","https://openalex.org/W2092313502","https://openalex.org/W2118078932","https://openalex.org/W2263170054","https://openalex.org/W2568327493","https://openalex.org/W3141151088"],"related_works":["https://openalex.org/W2515753295","https://openalex.org/W2334254610","https://openalex.org/W2500173965","https://openalex.org/W1976136035","https://openalex.org/W2606658789","https://openalex.org/W126356357","https://openalex.org/W2025874976","https://openalex.org/W2177716748","https://openalex.org/W1974298661","https://openalex.org/W2516370737"],"abstract_inverted_index":{"We":[0],"consider":[1],"numerical":[2,29],"approximations":[3,59],"of":[4,17,52,60,76],"incompressible":[5],"Newtonian":[6],"fluids":[7],"having":[8],"variable,":[9],"possibly":[10],"discontinuous,":[11],"density":[12,22,54],"and":[13,23,55],"viscosity.":[14],"Since":[15],"solutions":[16,41,79],"the":[18,35,44,50,53,61,66,69],"equations":[19],"with":[20],"variable":[21],"viscosity":[24],"may":[25,31],"not":[26,32,72],"be":[27],"unique,":[28,38,73],"schemes":[30],"converge.":[33],"If":[34,68],"solution":[36,70],"is":[37,71],"then":[39],"approximate":[40,49,78],"computed":[42],"using":[43],"discontinuous":[45],"Galerkin":[46],"method":[47],"to":[48,65,82],"convection":[51],"stable":[56],"finite":[57],"element":[58],"momentum":[62],"equation":[63],"converge":[64,81],"solution.":[67,84],"a":[74,83],"subsequence":[75],"these":[77],"will":[80]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
