{"id":"https://openalex.org/W4401336255","doi":"https://doi.org/10.1063/5.0217658","title":"Stabilization of interconnected models with Nitsche's interface conditions using the two-grid approach: A finite element study","display_name":"Stabilization of interconnected models with Nitsche's interface conditions using the two-grid approach: A finite element study","publication_year":2024,"publication_date":"2024-08-01","ids":{"openalex":"https://openalex.org/W4401336255","doi":"https://doi.org/10.1063/5.0217658"},"language":"en","primary_location":{"id":"doi:10.1063/5.0217658","doi":"https://doi.org/10.1063/5.0217658","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0217658","pdf_url":null,"source":{"id":"https://openalex.org/S22862804","display_name":"Physics of Fluids","issn_l":"1070-6631","issn":["1070-6631","1089-7666","1527-2435"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics of Fluids","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5057610503","display_name":"Shahid Hussain","orcid":"https://orcid.org/0000-0001-5426-2290","observed_orcids":["https://orcid.org/0000-0001-5426-2290"]},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shahid Hussain","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112415151","display_name":"Md. Abdullah Al Mahbub","orcid":"https://orcid.org/0000-0002-5821-842X","observed_orcids":["https://orcid.org/0000-0002-5821-842X"]},"institutions":[{"id":"https://openalex.org/I288011450","display_name":"Comilla University","ror":"https://ror.org/02bnddg69","country_code":"BD","type":"education","lineage":["https://openalex.org/I288011450"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Md. Abdullah Al Mahbub","raw_affiliation_strings":["Department of Mathematics, Comilla University 2 , Cumilla 3506, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Comilla University 2 , Cumilla 3506, Bangladesh","institution_ids":["https://openalex.org/I288011450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028639093","display_name":"Xinlong Feng","orcid":"https://orcid.org/0000-0002-5354-6424","observed_orcids":["https://orcid.org/0000-0002-5354-6424"]},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinlong Feng","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China"],"raw_orcid":"https://orcid.org/0000-0002-5354-6424","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109972411","display_name":"Fateh Ali Rana","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fateh Ali Rana","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University 1 , Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101937508","display_name":"Fazal Haq","orcid":"https://orcid.org/0000-0002-9860-5707","observed_orcids":["https://orcid.org/0000-0002-9860-5707"]},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Fazal Haq","raw_affiliation_strings":["Department of Mathematics Karakoram International University Main Campus 3 , Gilgit 15100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-9860-5707","affiliations":[{"raw_affiliation_string":"Department of Mathematics Karakoram International University Main Campus 3 , Gilgit 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014361802","display_name":"Arshad Hussain","orcid":"https://orcid.org/0000-0001-5941-4564","observed_orcids":["https://orcid.org/0000-0001-5941-4564"]},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Arshad Hussain","raw_affiliation_strings":["Karakoram International University 4 , Hunza Campus, Hunza 15700, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5941-4564","affiliations":[{"raw_affiliation_string":"Karakoram International University 4 , Hunza Campus, Hunza 15700, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101937508"],"corresponding_institution_ids":["https://openalex.org/I236232284"],"apc_list":null,"apc_paid":null,"fwci":1.4255,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75239234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"36","issue":"8","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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.0,"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/two-grid-method","display_name":"two-grid method","score":0.8650000095367432},{"id":"https://openalex.org/keywords/fluid-fluid-interaction","display_name":"fluid-fluid interaction","score":0.9380000233650208},{"id":"https://openalex.org/keywords/domain-decomposition","display_name":"domain decomposition","score":0.5910000205039978},{"id":"https://openalex.org/keywords/interface-problems","display_name":"interface problems","score":0.4390000104904175},{"id":"https://openalex.org/keywords/multigrid-methods","display_name":"multigrid methods","score":0.6140000224113464},{"id":"https://openalex.org/keywords/mesh-independence","display_name":"mesh independence","score":0.7480000257492065},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.4970000088214874},{"id":"https://openalex.org/keywords/fluid-structure-interaction","display_name":"fluid-structure interaction","score":0.6060000061988831}],"concepts":[{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6529505848884583},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.6026447415351868},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5592411756515503},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5324310660362244},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.530786395072937},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5201685428619385},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5148593783378601},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.48944368958473206},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48882099986076355},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4792728126049042},{"id":"https://openalex.org/C2779126057","wikidata":"https://www.wikidata.org/wiki/Q478010","display_name":"Fluid\u2013structure interaction","level":3,"score":0.46925637125968933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45841026306152344},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4483293294906616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.437064528465271},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4048477113246918},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.29459336400032043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20859628915786743},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1753966510295868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1071384847164154},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.09662270545959473},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/5.0217658","doi":"https://doi.org/10.1063/5.0217658","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0217658","pdf_url":null,"source":{"id":"https://openalex.org/S22862804","display_name":"Physics of Fluids","issn_l":"1070-6631","issn":["1070-6631","1089-7666","1527-2435"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics of Fluids","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W70665148","https://openalex.org/W851665502","https://openalex.org/W1988235001","https://openalex.org/W1989997498","https://openalex.org/W1992695159","https://openalex.org/W2026178626","https://openalex.org/W2032246227","https://openalex.org/W2032778497","https://openalex.org/W2036681321","https://openalex.org/W2066014352","https://openalex.org/W2083689274","https://openalex.org/W2108914822","https://openalex.org/W2125508055","https://openalex.org/W2419852013","https://openalex.org/W2498071357","https://openalex.org/W2519809374","https://openalex.org/W2790917702","https://openalex.org/W2885611274","https://openalex.org/W2904831720","https://openalex.org/W2957828897","https://openalex.org/W2981369605","https://openalex.org/W3003752912","https://openalex.org/W3162521866","https://openalex.org/W3164797527","https://openalex.org/W3216208143","https://openalex.org/W4281687971","https://openalex.org/W4281760542","https://openalex.org/W4290635536","https://openalex.org/W4295585635","https://openalex.org/W4323048644","https://openalex.org/W4366990872","https://openalex.org/W4377021363","https://openalex.org/W4386695615","https://openalex.org/W4388086903","https://openalex.org/W4390586352","https://openalex.org/W4391046008","https://openalex.org/W4392028964","https://openalex.org/W4392438828","https://openalex.org/W4396595994","https://openalex.org/W4396902342","https://openalex.org/W4397013211"],"related_works":["https://openalex.org/W4281760542","https://openalex.org/W2017605853","https://openalex.org/W612415119","https://openalex.org/W4411236272","https://openalex.org/W4404391210","https://openalex.org/W7100249091","https://openalex.org/W295410927","https://openalex.org/W3150667068","https://openalex.org/W4407731033","https://openalex.org/W2068543868"],"abstract_inverted_index":{"In":[0],"this":[1,97,128],"paper,":[2],"a":[3,148,153],"stabilized":[4],"Stokes\u2013Stokes":[5],"system":[6],"with":[7,80,147],"Nitsche's":[8,38],"type":[9],"interface":[10,39,55,61,87,108],"conditions":[11,15,40,46,88],"is":[12,69,100,137,175,186],"presented.":[13],"These":[14],"are":[16],"commonly":[17],"employed":[18],"in":[19],"many":[20],"multi-physical":[21,34],"fields,":[22],"including":[23,103],"fluid\u2013fluid":[24,92],"interaction,":[25,27],"fluid\u2013structure":[26],"oceanographic":[28],"modeling,":[29,57],"and":[30,63,65,75,109,145,156,163,174,190],"atmospheric":[31],"forecasting.":[32],"For":[33],"domain":[35,112],"modeling":[36],"purposes,":[37],"provide":[41],"useful":[42],"benefits":[43],"over":[44],"classical":[45],"via":[47],"addressing":[48],"the":[49,91,107,111,114,120,184,197],"complicated":[50],"nature":[51],"of":[52,152,183,202],"fluid":[53],"phase":[54,58],"mathematical":[56],"boundary":[59],"tracking,":[60],"interactions,":[62],"mass":[64],"energy":[66],"transportation.":[67],"It":[68],"not":[70],"easy":[71],"to":[72,89,95,130],"find":[73,134],"analytical":[74],"numerical":[76,193,203],"solutions":[77],"for":[78,161,177],"models":[79],"these":[81],"characteristics.":[82],"We":[83],"use":[84],"more":[85],"accurate":[86],"solve":[90],"interaction":[93],"model":[94,198],"accomplish":[96],"numerically.":[98,191],"This":[99],"achieved":[101],"by":[102],"new":[104],"terms":[105],"at":[106],"decoupling":[110],"through":[113,199],"two-grid":[115],"technique,":[116],"which":[117],"ultimately":[118],"reduces":[119],"main":[121],"issue":[122],"into":[123],"several":[124],"smaller":[125],"problems.":[126,165],"Comparing":[127],"method":[129],"existing":[131],"models,":[132],"we":[133],"that":[135],"it":[136,141,167],"computationally":[138],"feasible":[139],"because":[140],"uses":[142],"less":[143],"memory":[144],"operates":[146],"coarse":[149],"grid":[150,155],"instead":[151],"fine":[154],"thus":[157],"improves":[158],"convergence":[159],"rates":[160],"complex":[162],"nonlinear":[164],"Furthermore,":[166],"shows":[168],"mesh":[169],"independence,":[170],"supports":[171],"potential":[172],"parallelization,":[173],"crucial":[176],"advanced":[178],"multigrid":[179],"techniques.":[180],"The":[181,192],"optimality":[182],"error":[185],"confirmed":[187],"both":[188],"theoretically":[189],"experimental":[194],"section":[195],"validates":[196],"three":[200],"types":[201],"experiments.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-08-06T00:00:00"}