{"id":"https://openalex.org/W4410063568","doi":"https://doi.org/10.1515/cmam-2024-0187","title":"Mapped Coercivity for the Stationary Navier\u2013Stokes Equations and Their Finite Element Approximations","display_name":"Mapped Coercivity for the Stationary Navier\u2013Stokes Equations and Their Finite Element Approximations","publication_year":2025,"publication_date":"2025-04-30","ids":{"openalex":"https://openalex.org/W4410063568","doi":"https://doi.org/10.1515/cmam-2024-0187"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2024-0187","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0187","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5054387983","display_name":"Roland Becker","orcid":null},"institutions":[{"id":"https://openalex.org/I144889574","display_name":"Universit\u00e9 de Pau et des Pays de l'Adour","ror":"https://ror.org/01frn9647","country_code":"FR","type":"education","lineage":["https://openalex.org/I144889574"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Roland Becker","raw_affiliation_strings":["Department of Mathematics , Universit\u00e9 de Pau et de l\u2019Adour (UPPA) , Avenue de l\u2019Universit\u00e9, BP 1155, 64013 Pau CEDEX , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Universit\u00e9 de Pau et de l\u2019Adour (UPPA) , Avenue de l\u2019Universit\u00e9, BP 1155, 64013 Pau CEDEX , France","institution_ids":["https://openalex.org/I144889574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064837569","display_name":"Malte Braack","orcid":"https://orcid.org/0000-0003-1730-6316"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Malte Braack","raw_affiliation_strings":["Mathematical Seminar , 90299 Kiel University , Heinrich-Hecht-Platz 6, 24098 Kiel , Germany"],"raw_orcid":"https://orcid.org/0000-0003-1730-6316","affiliations":[{"raw_affiliation_string":"Mathematical Seminar , 90299 Kiel University , Heinrich-Hecht-Platz 6, 24098 Kiel , Germany","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054387983"],"corresponding_institution_ids":["https://openalex.org/I144889574"],"apc_list":null,"apc_paid":null,"fwci":5.9701,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.96320695,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"25","issue":"3","first_page":"547","last_page":"560"},"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":0.9998000264167786,"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":0.9987999796867371,"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/finite-element-method","display_name":"Finite element method","score":0.7370768785476685},{"id":"https://openalex.org/keywords/coercivity","display_name":"Coercivity","score":0.692720353603363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45614856481552124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4138241112232208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3906610906124115},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.32035496830940247},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26612067222595215},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12589696049690247},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.05684089660644531}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7370768785476685},{"id":"https://openalex.org/C126530901","wikidata":"https://www.wikidata.org/wiki/Q432635","display_name":"Coercivity","level":2,"score":0.692720353603363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45614856481552124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4138241112232208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3906610906124115},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.32035496830940247},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26612067222595215},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12589696049690247},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.05684089660644531}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/cmam-2024-0187","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0187","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05297262v1","is_oa":false,"landing_page_url":"https://univ-pau.hal.science/hal-05297262","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Methods in Applied Mathematics, 2025, 25 (3), pp.547-560. &#x27E8;10.1515/cmam-2024-0187&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1545761024","https://openalex.org/W1708679080","https://openalex.org/W1778185943","https://openalex.org/W1972368368","https://openalex.org/W2047049009","https://openalex.org/W2058567087","https://openalex.org/W2095399846","https://openalex.org/W2158856246","https://openalex.org/W2161118855","https://openalex.org/W2985272081","https://openalex.org/W4252104256","https://openalex.org/W4254400231","https://openalex.org/W4301021743","https://openalex.org/W4408185851"],"related_works":["https://openalex.org/W1979864087","https://openalex.org/W2044642251","https://openalex.org/W3093027776","https://openalex.org/W1986796332","https://openalex.org/W4283367861","https://openalex.org/W2909854803","https://openalex.org/W850259343","https://openalex.org/W2609179044","https://openalex.org/W2022128204","https://openalex.org/W3015996521"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"addresses":[3],"the":[4,8,20,104,107,114,127],"challenge":[5],"of":[6,10,97,138,140],"proving":[7],"existence":[9,96,139],"solutions":[11,141],"for":[12,142,173,187],"nonlinear":[13,41,58,122,175],"equations":[14,22],"in":[15,38,71,90,190],"Banach":[16,72],"spaces,":[17,73],"focusing":[18],"on":[19],"Navier\u2013Stokes":[21,145],"and":[23,32,78,95,110,155,177,183],"their":[24,178],"discretizations.":[25,46,81],"Traditional":[26],"methods,":[27],"such":[28],"as":[29,117],"monotonicity-based":[30],"approaches":[31],"fixed-point":[33],"theorems,":[34],"often":[35],"face":[36],"limitations":[37],"handling":[39],"general":[40],"operators":[42,59],"or":[43],"finite":[44,79,146],"element":[45,80,147],"A":[47],"novel":[48],"concept,":[49],"mapped":[50,111,130],"coercivity,":[51,112],"provides":[52],"a":[53,61,118,152,170,185],"unifying":[54],"framework":[55,128],"to":[56,68,87,129,163],"analyze":[57],"through":[60],"continuous":[62],"mapping.":[63],"We":[64],"apply":[65],"these":[66],"ideas":[67],"saddle-point":[69,123],"problems":[70],"emphasizing":[74],"both":[75],"infinite-dimensional":[76],"formulations":[77],"Our":[82],"analysis":[83],"includes":[84],"stabilization":[85,158],"techniques":[86],"restore":[88],"coercivity":[89,131],"finite-dimensional":[91],"settings,":[92],"ensuring":[93],"stability":[94],"solutions.":[98],"For":[99,121],"linear":[100],"problems,":[101],"we":[102,125],"explore":[103],"relationship":[105],"between":[106],"inf-sup":[108],"condition":[109],"using":[113],"Stokes":[115],"equation":[116],"case":[119],"study.":[120],"systems,":[124],"extend":[126],"via":[132],"surjective":[133],"mappings,":[134],"enabling":[135],"concise":[136],"proofs":[137],"various":[143],"stabilized":[144],"methods.":[148],"These":[149],"include":[150],"Brezzi\u2013Pitk\u00e4ranta,":[151],"simple":[153],"variant,":[154],"local":[156],"projection":[157],"(LPS)":[159],"techniques,":[160],"with":[161],"extensions":[162],"convection-dominant":[164],"flows.":[165],"The":[166],"proposed":[167],"methodology":[168],"offers":[169],"robust":[171],"tool":[172],"analyzing":[174],"PDEs":[176],"discretizations,":[179],"bypassing":[180],"traditional":[181],"decompositions":[182],"providing":[184],"foundation":[186],"future":[188],"developments":[189],"computational":[191],"fluid":[192],"dynamics.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
