{"id":"https://openalex.org/W4416895691","doi":"https://doi.org/10.48550/arxiv.2507.01296","title":"Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations","display_name":"Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations","publication_year":2025,"publication_date":"2025-07-02","ids":{"openalex":"https://openalex.org/W4416895691","doi":"https://doi.org/10.48550/arxiv.2507.01296"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.01296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.01296","pdf_url":"https://arxiv.org/pdf/2507.01296","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.01296","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025261220","display_name":"Fukeng Huang","orcid":"https://orcid.org/0000-0003-3644-268X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Fukeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028981574","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-4885-5732"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Jie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.763700008392334,"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":0.763700008392334,"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":0.08330000191926956,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.03370000049471855,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7401999831199646},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6782000064849854},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6718000173568726},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5259000062942505},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.517799973487854},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4553000032901764},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.43860000371932983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7608000040054321},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7401999831199646},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6782000064849854},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6718000173568726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.63919997215271},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5259000062942505},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.517799973487854},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4000000059604645},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.29829999804496765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2906999886035919},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2752000093460083}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.01296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.01296","pdf_url":"https://arxiv.org/pdf/2507.01296","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.01296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.01296","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.01296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.01296","pdf_url":"https://arxiv.org/pdf/2507.01296","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"new":[1,123],"class":[2],"of":[3],"fully":[4,88],"decoupled":[5],"consistent":[6],"splitting":[7],"schemes":[8,21,93,109,127],"for":[9,48,86,94],"the":[10,25,49,80,95,105,112,122],"Navier-Stokes":[11,96],"equations":[12],"are":[13,22,58,79,100,117,131],"constructed":[14],"and":[15,52,65,74,83,107,125,134],"analyzed":[16],"in":[17,61,71],"this":[18],"paper.":[19],"The":[20],"based":[23,110],"on":[24,111],"Taylor":[26],"expansion":[27],"at":[28],"$t^{n+\u03b2}$":[29],"with":[30,128],"$\u03b2\\ge":[31],"1$":[32],"being":[33],"a":[34,62],"free":[35],"parameter.":[36],"It":[37],"is":[38],"shown":[39],"that":[40,104],"by":[41],"choosing":[42],"{\\color{black}":[43],"$\u03b2=":[44],"3,":[45],"\\,6,\\,9$}":[46],"respectively":[47],"second-,":[50],"third-":[51,106,124],"fourth-order":[53,108,126],"schemes,":[54],"their":[55],"numerical":[56],"solutions":[57],"uniformed":[59],"bounded":[60],"strong":[63],"norm,":[64],"admit":[66],"optimal":[67],"global-in-time":[68],"convergence":[69,84,138],"rates":[70],"both":[72],"2D":[73],"3D.":[75],"{\\color{black}These":[76],"}":[77],"results":[78,85,99],"first":[81],"stability":[82],"any":[87],"decoupled,":[89],"higher":[90],"than":[91],"second-order":[92],"equations.":[97],"Numerical":[98],"provided":[101],"to":[102,136],"show":[103],"usual":[113],"BDF":[114],"(i.e.":[115],"$\u03b2=1$)":[116],"not":[118],"unconditionally":[119,132],"stable":[120,133],"while":[121],"suitable":[129],"$\u03b2$":[130],"lead":[135],"expected":[137],"rates.":[139]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
