{"id":"https://openalex.org/W2784666651","doi":"https://doi.org/10.1137/16m1094233","title":"Asymptotic Preserving Error Estimates for Numerical Solutions of Compressible Navier--Stokes Equations in the Low Mach Number Regime","display_name":"Asymptotic Preserving Error Estimates for Numerical Solutions of Compressible Navier--Stokes Equations in the Low Mach Number Regime","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2784666651","doi":"https://doi.org/10.1137/16m1094233","mag":"2784666651"},"language":"en","primary_location":{"id":"doi:10.1137/16m1094233","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1094233","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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/A5074749816","display_name":"Eduard Feireisl","orcid":"https://orcid.org/0000-0002-3795-1315"},"institutions":[{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]},{"id":"https://openalex.org/I4396570518","display_name":"Institut de Math\u00e9matiques de Toulon","ror":"https://ror.org/038a20b58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I143002897","https://openalex.org/I4396570518"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Eduard Feireisl","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulon - EA 2134"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulon - EA 2134","institution_ids":["https://openalex.org/I143002897","https://openalex.org/I4396570518"]}]},{"author_position":"middle","author":{"id":null,"display_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1","raw_affiliation_strings":["Mathematical Institute [Praha] - Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute [Praha] - Academy of Sciences","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063077794","display_name":"\u0160\u00e1rka Ne\u010dasov\u00e1","orcid":"https://orcid.org/0000-0003-3853-4633"},"institutions":[{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"\u0160\u00e1rka Ne\u010dasov\u00e1","raw_affiliation_strings":["Technical University Hamburg Harburg [Hamburg]"],"affiliations":[{"raw_affiliation_string":"Technical University Hamburg Harburg [Hamburg]","institution_ids":["https://openalex.org/I884043246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107592038","display_name":"Anton\u00edn Novotn\u00fd","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Anton\u00edn Novotn\u00fd","raw_affiliation_strings":["Mathematical Institute [Praha] - Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute [Praha] - Academy of Sciences","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060096853","display_name":"Bangwei She","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bangwei She","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074749816"],"corresponding_institution_ids":["https://openalex.org/I143002897","https://openalex.org/I4396570518"],"apc_list":null,"apc_paid":null,"fwci":2.0801,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.84917793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"1","first_page":"150","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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":0.998199999332428,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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":0.6954218745231628},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5896148085594177},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5714300870895386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5352094769477844},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5340695977210999},{"id":"https://openalex.org/keywords/mach-number","display_name":"Mach number","score":0.5154162645339966},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.5015206336975098},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.46863698959350586},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.45314842462539673},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.45027321577072144},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31414610147476196},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14046066999435425},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06415513157844543}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6954218745231628},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5896148085594177},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5714300870895386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5352094769477844},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5340695977210999},{"id":"https://openalex.org/C165231844","wikidata":"https://www.wikidata.org/wiki/Q160669","display_name":"Mach number","level":2,"score":0.5154162645339966},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.5015206336975098},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.46863698959350586},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.45314842462539673},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.45027321577072144},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31414610147476196},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14046066999435425},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06415513157844543}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1094233","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1094233","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01810441v1","is_oa":false,"landing_page_url":"https://univ-tln.hal.science/hal-01810441","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2018, 16 (1), pp.150-183","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.699999988079071,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3076854100","display_name":null,"funder_award_id":"320078","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G4219685691","display_name":null,"funder_award_id":"16-03230S","funder_id":"https://openalex.org/F4320311333","funder_display_name":"Ministerstvo Vnitra \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320311333","display_name":"Ministerstvo Vnitra \u010cesk\u00e9 Republiky","ror":"https://ror.org/05w1nn565"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1714607903","https://openalex.org/W1967154621","https://openalex.org/W1994056581","https://openalex.org/W2013753235","https://openalex.org/W2014836614","https://openalex.org/W2023493249","https://openalex.org/W2027557220","https://openalex.org/W2029015215","https://openalex.org/W2030366749","https://openalex.org/W2073535540","https://openalex.org/W2080548630","https://openalex.org/W2081476622","https://openalex.org/W2082029579","https://openalex.org/W2090386503","https://openalex.org/W2103566196","https://openalex.org/W2108236244","https://openalex.org/W2138908501","https://openalex.org/W2147277530","https://openalex.org/W2150007097","https://openalex.org/W2161229398","https://openalex.org/W2464136807","https://openalex.org/W2528121553","https://openalex.org/W2582103697","https://openalex.org/W2963663115","https://openalex.org/W3099192173","https://openalex.org/W3100306894","https://openalex.org/W3112330256"],"related_works":["https://openalex.org/W4234264303","https://openalex.org/W2007246989","https://openalex.org/W2963059605","https://openalex.org/W2052669892","https://openalex.org/W2313597186","https://openalex.org/W1991751407","https://openalex.org/W2029290092","https://openalex.org/W2042362390","https://openalex.org/W2419332772","https://openalex.org/W4233568714"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,8,30,36,43,59,63,67,119,123,128,131,136,143],"convergence":[3,95],"of":[4,7,58,66,75,96,122,130],"numerical":[5,17,56,115,120],"solutions":[6],"compressible":[9,60,124],"Navier--Stokes":[10,69,133],"system":[11],"to":[12,127,148],"its":[13],"incompressible":[14,68,132],"limit.":[15],"The":[16,45,52],"solution":[18,57,65,121,129],"is":[19,71],"obtained":[20],"by":[21,73],"a":[22,55,76],"combined":[23],"finite":[24,33],"element--finite":[25],"volume":[26],"method":[27],"based":[28],"on":[29],"linear":[31],"Crouzeix--Raviart":[32],"element":[34],"for":[35,42,88],"velocity":[37],"and":[38,62,87,142],"piecewise":[39],"constant":[40],"approximation":[41],"density.":[44],"convective":[46],"terms":[47],"are":[48],"approximated":[49],"using":[50],"upwinding.":[51],"distance":[53],"between":[54],"problem":[61,125],"strong":[64],"equations":[70,134],"measured":[72],"means":[74],"relative":[77],"energy":[78],"functional.":[79],"For":[80],"barotropic":[81],"pressure":[82],"exponent":[83],"$\\gamma":[84],"\\geq":[85],"3/2$":[86],"well-prepared":[89],"initial":[90],"data":[91],"we":[92],"obtain":[93],"uniform":[94],"order":[97],"${\\cal":[98],"O}(\\sqrt{\\Delta":[99],"t},":[100],"h^a,":[101],"\\varepsilon)$,":[102],"$a":[103],"=":[104],"\\min":[105],"\\{":[106],"\\frac{2":[107],"\\gamma":[108],"-":[109],"3":[110],"}{":[111],"\\gamma},":[112],"1\\}$.":[113],"Extensive":[114],"simulations":[116],"confirm":[117],"that":[118],"converges":[126],"as":[135],"discretization":[137],"parameters":[138],"$\\Delta":[139],"t$,":[140],"$h$":[141],"Mach":[144],"number":[145],"$\\varepsilon$":[146],"tend":[147],"zero.":[149]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-30T08:08:38.191290","created_date":"2018-02-02T00:00:00"}
