{"id":"https://openalex.org/W4412567006","doi":"https://doi.org/10.1090/mcom/4126","title":"Unconditionally stable consistent splitting schemes for the Navier\u2013Stokes equations with \ud835\udc36\u2070 finite elements","display_name":"Unconditionally stable consistent splitting schemes for the Navier\u2013Stokes equations with \ud835\udc36\u2070 finite elements","publication_year":2025,"publication_date":"2025-07-22","ids":{"openalex":"https://openalex.org/W4412567006","doi":"https://doi.org/10.1090/mcom/4126"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4126","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4126","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5101247250","display_name":"Xu Li","orcid":null},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I127108677","display_name":"Eastern Institute of Technology","ror":"https://ror.org/00ct9cz38","country_code":"NZ","type":"education","lineage":["https://openalex.org/I127108677","https://openalex.org/I4387152882"]}],"countries":["CN","NZ"],"is_corresponding":false,"raw_author_name":"Xu Li","raw_affiliation_strings":["Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People\u2019s Republic of China; and School of Mathematical Sciences, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, People\u2019s Republic of China","Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People's Republic of China","School of Mathematical Sciences, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People\u2019s Republic of China; and School of Mathematical Sciences, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, People\u2019s Republic of China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People's Republic of China","institution_ids":["https://openalex.org/I127108677"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Jinzhai Road 96, Hefei 230026, People's Republic of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028981574","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-4885-5732"},"institutions":[{"id":"https://openalex.org/I127108677","display_name":"Eastern Institute of Technology","ror":"https://ror.org/00ct9cz38","country_code":"NZ","type":"education","lineage":["https://openalex.org/I127108677","https://openalex.org/I4387152882"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Jie Shen","raw_affiliation_strings":["Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People\u2019s Republic of China","Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People\u2019s Republic of China","institution_ids":["https://openalex.org/I127108677"]},{"raw_affiliation_string":"Eastern Institute for Advanced Study, Eastern Institute of Technology, Tongxin Road 568, Ningbo 315200, People's Republic of China","institution_ids":["https://openalex.org/I127108677"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12617578,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"362","first_page":"2669","last_page":"2694"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9987999796867371,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8883253931999207},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5037106871604919},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4662992060184479},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36794406175613403},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.08253774046897888},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.06698215007781982},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05363631248474121}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8883253931999207},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5037106871604919},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4662992060184479},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36794406175613403},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.08253774046897888},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.06698215007781982},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05363631248474121}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4126","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4126","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6300447137","display_name":null,"funder_award_id":"2024M751547","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W325210746","https://openalex.org/W1596838038","https://openalex.org/W1974221287","https://openalex.org/W1975039968","https://openalex.org/W1990225789","https://openalex.org/W1990698401","https://openalex.org/W1994968461","https://openalex.org/W2000915583","https://openalex.org/W2003408966","https://openalex.org/W2047859546","https://openalex.org/W2051708601","https://openalex.org/W2074252556","https://openalex.org/W2088018887","https://openalex.org/W2096130365","https://openalex.org/W2097830129","https://openalex.org/W2099200620","https://openalex.org/W2100675673","https://openalex.org/W2118922968","https://openalex.org/W2130350269","https://openalex.org/W2154153079","https://openalex.org/W2156946226","https://openalex.org/W2164622471","https://openalex.org/W2166614820","https://openalex.org/W2282835663","https://openalex.org/W2497754766","https://openalex.org/W2921770886","https://openalex.org/W3009015073","https://openalex.org/W3118262253","https://openalex.org/W3141019747","https://openalex.org/W3187902182","https://openalex.org/W3204708751","https://openalex.org/W4214489543","https://openalex.org/W4252104256","https://openalex.org/W4306181181","https://openalex.org/W4387742399"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0,93],"construct":[1],"in":[2,88],"this":[3],"paper":[4],"first-":[5],"and":[6,11,25,75,107,116],"second-order":[7],"(in":[8],"time)":[9],"decoupled":[10],"unconditionally":[12],"stable":[13],"schemes":[14],"for":[15,50,122],"the":[16,21,35,38,56,65,68,89,96,99,103,113,123],"Navier\u2013Stokes":[17],"equations":[18],"based":[19],"on":[20,67,98],"consistent":[22],"splitting":[23],"methods":[24],"C":[26],"0":[27],"C^0":[28],"finite":[29],"elements,":[30],"where":[31],"spatial":[32],"discontinuity":[33],"of":[34,37,58],"gradient":[36,57],"discrete":[39,59,91,105,126],"velocity":[40,60],"is":[41,54,61],"treated":[42],"using":[43],"a":[44],"discontinuous":[45,62],"Galerkin":[46],"framework.":[47],"The":[48],"challenge":[49],"their":[51],"stability":[52,115],"analysis":[53,121],"that":[55,64],"so":[63],"estimate":[66,97],"continuous":[69],"Stokes":[70,100],"pressure":[71,101],"by":[72],"Liu,":[73,74],"Pego":[76],"[Comm.":[77],"Pure":[78],"Appl.":[79],"Math.":[80],"60":[81],"(2007),":[82],"pp.":[83],"1443\u20131487]":[84],"cannot":[85],"be":[86],"applied":[87],"space":[90,104],"case.":[92],"first":[94],"extend":[95],"to":[102,111,132],"case,":[106],"then":[108],"use":[109],"it":[110],"prove":[112],"unconditional":[114],"carry":[117],"out":[118],"an":[119],"error":[120],"proposed":[124],"fully":[125],"schemes.":[127],"Numerical":[128],"results":[129],"are":[130],"presented":[131],"validate":[133],"our":[134],"analytical":[135],"results.":[136]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
