{"id":"https://openalex.org/W4415250630","doi":"https://doi.org/10.48550/arxiv.2509.16461","title":"Finite element approximation of the stationary Navier-Stokes problem with non-smooth data","display_name":"Finite element approximation of the stationary Navier-Stokes problem with non-smooth data","publication_year":2025,"publication_date":"2025-09-19","ids":{"openalex":"https://openalex.org/W4415250630","doi":"https://doi.org/10.48550/arxiv.2509.16461"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.16461","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.16461","pdf_url":"https://arxiv.org/pdf/2509.16461","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.16461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112409950","display_name":"Mar\u0131\u0301a G. Armentano","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Armentano, Mar\u00eda Gabriela","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5120024804","display_name":"Mauricio Mendiluce","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mendiluce, Mauricio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9943000078201294,"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":0.9943000078201294,"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":0.9869999885559082,"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/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9799000024795532,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6277999877929688},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6132000088691711},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45489999651908875},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.423799991607666},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4196999967098236},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4099000096321106},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4050999879837036},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.3711000084877014},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.36880001425743103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7197999954223633},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6277999877929688},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6132000088691711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5482000112533569},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43160000443458557},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4099000096321106},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.3711000084877014},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.36880001425743103},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.34540000557899475},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.33379998803138733},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.33009999990463257},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C65705168","wikidata":"https://www.wikidata.org/wiki/Q7100757","display_name":"Orders of approximation","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.28949999809265137},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C48395688","wikidata":"https://www.wikidata.org/wiki/Q6823714","display_name":"Method of fundamental solutions","level":5,"score":0.2687999904155731},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2509.16461","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.16461","pdf_url":"https://arxiv.org/pdf/2509.16461","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2509.16461","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2509.16461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.16461","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.16461","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.16461","pdf_url":"https://arxiv.org/pdf/2509.16461","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,23],"aim":[1],"of":[2,12,42,59,71,83],"this":[3,60],"work":[4],"is":[5,26],"to":[6,92],"analyze":[7],"the":[8,13,30,40,43,48,69,72,79,84],"finite":[9,80],"element":[10,81],"approximation":[11,25,70],"two-dimensional":[14],"stationary":[15],"Navier-Stokes":[16,31,49,73],"equations":[17],"with":[18,33,51,75,98],"non-smooth":[19,76],"Dirichlet":[20],"boundary":[21,36,53],"data.":[22],"discrete":[24],"obtained":[27],"by":[28],"considering":[29],"system":[32,50,74],"a":[34,56,64],"regularized":[35,86],"solution.":[37],"Based":[38],"on":[39],"existence":[41],"very":[44],"weak":[45],"solution":[46,82],"for":[47],"L2":[52],"data,":[54],"and":[55,78],"suitable":[57],"decomposition":[58],"solution,":[61],"we":[62],"obtain":[63],"priori":[65],"error":[66],"estimates":[67,89],"between":[68],"data":[77],"associated":[85],"problem.":[87],"These":[88],"allow":[90],"us":[91],"conclude":[93],"that":[94],"our":[95],"approach":[96],"converges":[97],"optimal":[99],"order.":[100]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-16T00:00:00"}
