{"id":"https://openalex.org/W4321482472","doi":"https://doi.org/10.1137/21m1450872","title":"Difference Finite Element Method for the 3D Steady Navier\u2013Stokes Equations","display_name":"Difference Finite Element Method for the 3D Steady Navier\u2013Stokes Equations","publication_year":2023,"publication_date":"2023-02-22","ids":{"openalex":"https://openalex.org/W4321482472","doi":"https://doi.org/10.1137/21m1450872"},"language":"en","primary_location":{"id":"doi:10.1137/21m1450872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450872","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/A5028639093","display_name":"Xinlong Feng","orcid":"https://orcid.org/0000-0002-5354-6424"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xinlong Feng","raw_affiliation_strings":["College of Mathematics and Systems Science & Institute of Mathematics and Physics, Xinjiang University, Urumqi 830046, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science & Institute of Mathematics and Physics, Xinjiang University, Urumqi 830046, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103503974","display_name":"Xiaoli Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoli Lu","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100457891","display_name":"Yinnian He","orcid":"https://orcid.org/0000-0003-3402-8493"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yinnian He","raw_affiliation_strings":["Corresponding author. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China, and School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"],"affiliations":[{"raw_affiliation_string":"Corresponding author. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China, and School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028639093"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5229,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.88313089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"61","issue":"1","first_page":"167","last_page":"193"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9986000061035156,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9901999831199646,"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/finite-element-method","display_name":"Finite element method","score":0.7352315187454224},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6643995642662048},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6234124898910522},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5798739790916443},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5444993376731873},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5019664764404297},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4680829644203186},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4549110233783722},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4286736249923706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2857198417186737},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.09375357627868652},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.065360426902771},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06228339672088623},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.060411274433135986}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7352315187454224},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6643995642662048},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6234124898910522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5798739790916443},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5444993376731873},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5019664764404297},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4680829644203186},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4549110233783722},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4286736249923706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2857198417186737},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.09375357627868652},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.065360426902771},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06228339672088623},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.060411274433135986},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1450872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450872","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1840540895","display_name":null,"funder_award_id":"2021KF02","funder_id":"https://openalex.org/F4320336345","funder_display_name":"State Key Laboratory of High Temperature Gas Dynamics"},{"id":"https://openalex.org/G1921437719","display_name":null,"funder_award_id":"12271465","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3023535629","display_name":null,"funder_award_id":"U19A2079","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3917965838","display_name":null,"funder_award_id":"12026257","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5659702248","display_name":null,"funder_award_id":"12071406","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336345","display_name":"State Key Laboratory of High Temperature Gas Dynamics","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1658203550","https://openalex.org/W1906754392","https://openalex.org/W1977424127","https://openalex.org/W2017301866","https://openalex.org/W2032772521","https://openalex.org/W2036207036","https://openalex.org/W2038671615","https://openalex.org/W2041179520","https://openalex.org/W2049873117","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2067047646","https://openalex.org/W2067392615","https://openalex.org/W2073256259","https://openalex.org/W2076582418","https://openalex.org/W2082187902","https://openalex.org/W2125000361","https://openalex.org/W2133248904","https://openalex.org/W2135123656","https://openalex.org/W2157785891","https://openalex.org/W2163119241","https://openalex.org/W2560636309","https://openalex.org/W2741560340","https://openalex.org/W2770422933","https://openalex.org/W2795226531","https://openalex.org/W2895096231","https://openalex.org/W2945197905","https://openalex.org/W2974757475","https://openalex.org/W3009848594","https://openalex.org/W4200005857","https://openalex.org/W4200394135","https://openalex.org/W4252104256","https://openalex.org/W4281485387","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W4402427056","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{".In":[0],"this":[1],"work,":[2],"a":[3,35,68,102],"difference":[4,130,152,184],"finite":[5,23,39,56,77,131,153,185,220],"element":[6,24,40,57,78,132,154,186],"method":[7,18,122,133],"for":[8,134],"the":[9,22,28,38,44,55,63,86,93,97,107,113,119,125,129,136,146,151,163,171,183,190,195,208,213],"3D":[10,87,103,137,164,196],"steady":[11,31,46,88,138,165,197],"Navier\u2013Stokes":[12,32,198],"equations":[13,33,168],"is":[14],"presented.":[15],"This":[16],"new":[17],"consists":[19],"of":[20,27,37,43,115,128,150,162,182,194,212],"transmitting":[21],"solution":[25,192],"\\((u_h,p_h)\\)":[26],"three-dimensional":[29],"(3D)":[30],"into":[34],"series":[36],"solutions":[41,155,187],"\\((u_h^{nk},p_h^{nk})\\)":[42],"2D":[45,69],"Oseen":[47,89,120,140,166],"iterative":[48,90,121,141,167,217],"equations,":[49,91],"which":[50],"are":[51,204],"solved":[52],"by":[53],"using":[54],"pair":[58,79,95],"\\((P^b_1,P^b_1,":[59],"P_1)\\times":[60,81],"P_1\\)":[61],"satisfying":[62],"discrete":[64,98],"inf-sup":[65,99,223],"condition":[66,100],"in":[67,101],"domain":[70,104],"\\(\\omega\\)":[71],".":[72],"In":[73],"addition,":[74],"we":[75,117,144],"use":[76],"\\(((P^b_1,P^b_1,P_1)\\times":[80],"(P_1\\times":[82],"P_0)\\)":[83],"to":[84,177,189,206],"solve":[85],"where":[92],"velocity-pressure":[94],"satisfies":[96],"\\(\\Omega\\)":[105],"under":[106],"quasi-uniform":[108],"mesh":[109,225],"condition.":[110],"To":[111],"overcome":[112],"difficulty":[114],"nonlinearity,":[116],"apply":[118],"and":[123,148,169,210],"present":[124],"weak":[126],"formulation":[127],"solving":[135],"\\(\\tau\\)":[139],"equations.":[142,199],"Moreover,":[143],"provide":[145],"existence":[147],"uniqueness":[149],"\\((u^n_h,p^n_h)=(\\sum":[156],"^{l_3}_{k=0}u_h^{nk}\\phi":[157],"_k(z),":[158],"\\sum":[159],"^{l_3}_{k=1}p_h^{nk}\\psi":[160],"_k(z))\\)":[161],"deduce":[170],"first":[172],"order":[173],"convergence":[174],"with":[175],"respect":[176],"\\((\\sigma":[178],"^{n+1},":[179],"\\tau,":[180],"h)\\)":[181],"\\((u^n_h,p^n_h)\\)":[188],"exact":[191],"\\((u,p)\\)":[193],"Finally,":[200],"some":[201],"numerical":[202],"tests":[203],"presented":[205],"show":[207],"accuracy":[209],"effectiveness":[211],"proposed":[214],"method.KeywordsNavier\u2013Stokes":[215],"equationsOseen":[216],"equationsweak":[218],"formulationdifference":[219],"elementerror":[221],"estimatediscrete":[222],"conditionquasi-uniform":[224],"conditionMSC":[226],"codes76D0765N0665N3065N15":[227]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}