{"id":"https://openalex.org/W2035829942","doi":"https://doi.org/10.1137/s1064827598347411","title":"On Schwarz Alternating Methods for the Incompressible Navier--Stokes Equations","display_name":"On Schwarz Alternating Methods for the Incompressible Navier--Stokes Equations","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2035829942","doi":"https://doi.org/10.1137/s1064827598347411","mag":"2035829942"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827598347411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598347411","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5003813327","display_name":"S. H. Lui","orcid":"https://orcid.org/0000-0003-2024-5817"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. H. Lui","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003813327"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3025,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.95199709,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"22","issue":"6","first_page":"1974","last_page":"1986"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.8792034387588501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.87632155418396},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.8632926940917969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.601891815662384},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.543061375617981},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5113701224327087},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.49867773056030273},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.49108266830444336},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.439790815114975},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.3619019687175751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32186955213546753},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.24545589089393616},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20609316229820251},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1367572546005249},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06969717144966125},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06840857863426208}],"concepts":[{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.8792034387588501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.87632155418396},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.8632926940917969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.601891815662384},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.543061375617981},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5113701224327087},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.49867773056030273},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49108266830444336},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.439790815114975},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3619019687175751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32186955213546753},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.24545589089393616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20609316229820251},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1367572546005249},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06969717144966125},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06840857863426208},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827598347411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598347411","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.6910","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.6910","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ust.hk/~shlui/34741.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W105972517","https://openalex.org/W1973685600","https://openalex.org/W1975113089","https://openalex.org/W2068628100","https://openalex.org/W2092422489","https://openalex.org/W2122824057","https://openalex.org/W2151718183","https://openalex.org/W2477040106"],"related_works":["https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2493580937","https://openalex.org/W2233890230","https://openalex.org/W132556536"],"abstract_inverted_index":{"The":[0,24],"Schwarz":[1,54,73],"alternating":[2,55],"method":[3],"can":[4],"be":[5],"used":[6],"to":[7,76],"solve":[8],"linear":[9],"elliptic":[10,41],"boundary":[11,42],"value":[12,43],"problems":[13,44],"on":[14],"domains":[15],"which":[16,34],"consist":[17],"of":[18,32,40,47],"two":[19],"or":[20],"more":[21],"overlapping":[22],"subdomains.":[23,49],"solution":[25,79],"is":[26,69,85],"approximated":[27],"by":[28],"an":[29],"infinite":[30],"sequence":[31,39],"functions":[33],"result":[35],"from":[36],"solving":[37],"a":[38],"in":[45],"each":[46],"the":[48,58,72,77,82],"This":[50],"paper":[51],"considers":[52],"four":[53],"methods":[56],"for":[57],"N-dimensional,":[59],"steady,":[60],"viscous,":[61],"incompressible":[62],"Navier--Stokes":[63],"equations,":[64],"$N":[65],"\\leq":[66],"4$.":[67],"It":[68],"shown":[70],"that":[71,81],"sequences":[74],"converge":[75],"true":[78],"provided":[80],"Reynolds":[83],"number":[84],"sufficiently":[86],"small.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}