{"id":"https://openalex.org/W7212054482","doi":"https://doi.org/10.48550/arxiv.2609.07527","title":"Analysis of a Surface Crouzeix-Raviart Element for the Stokes Problem","display_name":"Analysis of a Surface Crouzeix-Raviart Element for the Stokes Problem","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212054482","doi":"https://doi.org/10.48550/arxiv.2609.07527"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.07527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07527","pdf_url":"https://arxiv.org/pdf/2609.07527","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.07527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061539420","display_name":"Manisha Chowdhury","orcid":"https://orcid.org/0000-0001-5079-4513","observed_orcids":["https://orcid.org/0000-0001-5079-4513"]},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Chowdhury, Manisha","raw_affiliation_strings":["Institute of Analysis and Numerics , Otto-von-Guericke University Magdeburg , Universit\u00e4tsplatz 2 , 39106 Magdeburg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Numerics , Otto-von-Guericke University Magdeburg , Universit\u00e4tsplatz 2 , 39106 Magdeburg , Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016944304","display_name":"Carolin Mehlmann","orcid":"https://orcid.org/0000-0001-7329-5178","observed_orcids":["https://orcid.org/0000-0001-7329-5178"]},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mehlmann, Carolin","raw_affiliation_strings":["Institute of Analysis and Numerics , Otto-von-Guericke University Magdeburg , Universit\u00e4tsplatz 2 , 39106 Magdeburg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Numerics , Otto-von-Guericke University Magdeburg , Universit\u00e4tsplatz 2 , 39106 Magdeburg , Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/crouzeix-raviart-element","display_name":"Crouzeix-Raviart element","score":0.8960000276565552},{"id":"https://openalex.org/keywords/nonconforming-finite-elements","display_name":"nonconforming finite elements","score":0.9660000205039978},{"id":"https://openalex.org/keywords/curved-surfaces","display_name":"curved surfaces","score":0.7739999890327454},{"id":"https://openalex.org/keywords/spurious-oscillations","display_name":"spurious oscillations","score":0.777999997138977},{"id":"https://openalex.org/keywords/inf-sup-stability","display_name":"inf-sup stability","score":0.6610000133514404},{"id":"https://openalex.org/keywords/a-priori-error-estimates","display_name":"a priori error estimates","score":0.9049999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627000212669373},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.696399986743927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6559000015258789},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6080999970436096},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5925999879837036},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48339998722076416},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4666999876499176},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.41620001196861267},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.3912999927997589},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.3479999899864197},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C153919410","wikidata":"https://www.wikidata.org/wiki/Q9993851","display_name":"Weak formulation","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.31310001015663147},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3052999973297119},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.28839999437332153},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.25999999046325684}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.07527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07527","pdf_url":"https://arxiv.org/pdf/2609.07527","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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.2609.07527","doi":"https://doi.org/10.48550/arxiv.2609.07527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.07527","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.07527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07527","pdf_url":"https://arxiv.org/pdf/2609.07527","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212054482.pdf","grobid_xml":"https://content.openalex.org/works/W7212054482.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4405960563","https://openalex.org/W1540761592","https://openalex.org/W2855016263","https://openalex.org/W2052547118","https://openalex.org/W7095729049","https://openalex.org/W7212067430","https://openalex.org/W2616382513","https://openalex.org/W7154469363","https://openalex.org/W7214277745","https://openalex.org/W1993452929"],"abstract_inverted_index":{"Recently,":[0],"increasing":[1],"attention":[2],"has":[3],"been":[4],"paid":[5],"to":[6,79],"finite":[7,46,76,131],"element":[8,47,132],"discretizations":[9],"of":[10,52,112,134],"vector-valued":[11],"flow":[12],"problems":[13],"posed":[14],"on":[15,28,48,92],"curved":[16],"surfaces.":[17],"In":[18],"this":[19,123,130],"work,":[20],"we":[21,127,146],"study":[22],"a":[23,29,43,49],"surface":[24,37],"Stokes":[25],"system":[26],"defined":[27],"two-dimensional":[30],"manifold":[31],"embedded":[32],"in":[33,82,152],"three-dimensional":[34],"space.":[35,95],"The":[36,64],"velocity":[38,84,135],"field":[39,85],"is":[40,58],"approximated":[41],"using":[42],"nonconforming":[44,94],"Crouzeix-Raviart":[45,75],"polyhedral":[50],"approximation":[51,73],"the":[53,56,68,83,87,93,99,110,113,117,140,154,158],"surface,":[54],"while":[55],"pressure":[57,137],"discretized":[59],"by":[60,102,165],"piecewise":[61],"constant":[62],"functions.":[63],"governing":[65],"equations":[66],"involve":[67],"symmetric":[69],"strain-rate":[70],"tensor,":[71],"whose":[72],"with":[74],"elements":[77],"leads":[78],"spurious":[80],"oscillations":[81],"because":[86],"discrete":[88,118,141],"Korn":[89,119],"inequality":[90,120],"fails":[91],"We":[96],"therefore":[97],"stabilize":[98],"momentum":[100],"equation":[101],"adding":[103],"an":[104],"edge-jump":[105],"penalty":[106],"term,":[107],"which":[108],"restores":[109],"coervity":[111],"bilinear":[114],"term":[115],"as":[116],"holds":[121],"for":[122],"stabilized":[124],"version.":[125],"Additionally,":[126],"establish":[128],"that":[129],"pair":[133],"and":[136,157],"spaces":[138],"satisfies":[139],"inf-sup":[142],"compatibility":[143],"condition.":[144],"Furthermore,":[145],"derive":[147],"optimal":[148],"a-priori":[149],"error":[150],"estimates":[151],"both":[153],"energy":[155],"norm":[156],"$L^2$-norm.":[159],"These":[160],"theoretical":[161],"results":[162],"are":[163],"corroborated":[164],"numerical":[166],"experiments.":[167]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-10T00:00:00"}