{"id":"https://openalex.org/W2551282305","doi":"https://doi.org/10.1137/16m1076526","title":"A Discrete Data Assimilation Scheme for the Solutions of the Two-Dimensional Navier--Stokes Equations and Their Statistics","display_name":"A Discrete Data Assimilation Scheme for the Solutions of the Two-Dimensional Navier--Stokes Equations and Their Statistics","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2551282305","doi":"https://doi.org/10.1137/16m1076526","mag":"2551282305"},"language":"en","primary_location":{"id":"doi:10.1137/16m1076526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1076526","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","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/A5109484843","display_name":"Ciprian Foia\u015f","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ciprian Foias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079585562","display_name":"Cecilia F. Mondaini","orcid":"https://orcid.org/0000-0002-6880-2814"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cecilia F. Mondaini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076835339","display_name":"Edriss S. Titi","orcid":"https://orcid.org/0000-0002-5004-1746"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edriss S. Titi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.1067,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.98476198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"15","issue":"4","first_page":"2109","last_page":"2142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11459","display_name":"Arctic and Antarctic ice dynamics","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.7348530292510986},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5771125555038452},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5097221732139587},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4668714702129364},{"id":"https://openalex.org/keywords/downscaling","display_name":"Downscaling","score":0.44533753395080566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3569926619529724}],"concepts":[{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.7348530292510986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5771125555038452},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5097221732139587},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4668714702129364},{"id":"https://openalex.org/C41156917","wikidata":"https://www.wikidata.org/wiki/Q682831","display_name":"Downscaling","level":3,"score":0.44533753395080566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3569926619529724},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C132651083","wikidata":"https://www.wikidata.org/wiki/Q7942","display_name":"Climate change","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1076526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1076526","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt3191m5pk","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/3191m5pk","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, vol 15, iss 4","raw_type":"article"},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/184765","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/184765","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1973875859","display_name":null,"funder_award_id":"N00014-15-1-2333","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2024360659","display_name":"Collaborative Research: Mathematical Analysis of Certain Geophysical and Fluid Dynamics Models","funder_award_id":"1109640","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3078313421","display_name":null,"funder_award_id":"N00014-15-1-2333","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3813791885","display_name":null,"funder_award_id":"203552/2014-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4719905851","display_name":null,"funder_award_id":"DMS-1109645","funder_id":"https://openalex.org/F4320337436","funder_display_name":"Division of Grants and Agreements"},{"id":"https://openalex.org/G5255701651","display_name":"Collaborative Research: Study of Turbulence in Physical Systems Through Complex Singularities and Determining Modes","funder_award_id":"1109645","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G925587833","display_name":null,"funder_award_id":"DMS-1109640","funder_id":"https://openalex.org/F4320337436","funder_display_name":"Division of Grants and Agreements"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337436","display_name":"Division of Grants and Agreements","ror":"https://ror.org/014eweh95"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W106245569","https://openalex.org/W1532495845","https://openalex.org/W1539881364","https://openalex.org/W1570440531","https://openalex.org/W1573860137","https://openalex.org/W1596195796","https://openalex.org/W1925472001","https://openalex.org/W1969298725","https://openalex.org/W1979749650","https://openalex.org/W1980617250","https://openalex.org/W1986755923","https://openalex.org/W2004124997","https://openalex.org/W2005193783","https://openalex.org/W2008079423","https://openalex.org/W2012912447","https://openalex.org/W2021956888","https://openalex.org/W2023480419","https://openalex.org/W2026172681","https://openalex.org/W2035587664","https://openalex.org/W2041354515","https://openalex.org/W2047417234","https://openalex.org/W2048551346","https://openalex.org/W2065297008","https://openalex.org/W2066949116","https://openalex.org/W2084338811","https://openalex.org/W2088417707","https://openalex.org/W2112550298","https://openalex.org/W2128396151","https://openalex.org/W2131920939","https://openalex.org/W2154133935","https://openalex.org/W2168899527","https://openalex.org/W2175869447","https://openalex.org/W2179596748","https://openalex.org/W2324610639","https://openalex.org/W2962760563","https://openalex.org/W2963913058","https://openalex.org/W3099034578","https://openalex.org/W3101512171","https://openalex.org/W3104096483","https://openalex.org/W3104728148","https://openalex.org/W3125802632","https://openalex.org/W4250645666"],"related_works":["https://openalex.org/W2394436593","https://openalex.org/W3013458534","https://openalex.org/W3010558748","https://openalex.org/W2526815458","https://openalex.org/W4220911053","https://openalex.org/W2380042710","https://openalex.org/W2944582722","https://openalex.org/W4377833746","https://openalex.org/W2369988800","https://openalex.org/W4287905284"],"abstract_inverted_index":{"We":[0],"adapt":[1],"a":[2,44,114],"previously":[3],"introduced":[4],"continuous":[5],"in":[6,28,85,104],"time":[7,29,76,86],"data":[8,131],"assimilation":[9,132],"(downscaling)":[10],"algorithm":[11,38,133],"for":[12],"the":[13,18,23,66,70,75,89,92,96,102,119,122],"two-dimensional":[14],"Navier--Stokes":[15],"equations":[16],"to":[17,41,101,113],"more":[19],"realistic":[20],"case":[21],"when":[22],"measurements":[24],"are":[25],"obtained":[26],"discretely":[27],"and":[30,54,74,95],"may":[31],"be":[32],"contaminated":[33],"by":[34],"systematic":[35],"errors.":[36,123],"Our":[37],"is":[39,134],"designed":[40],"work":[42],"with":[43],"general":[45],"class":[46],"of":[47,88,121,128],"observables,":[48],"such":[49],"as":[50],"low":[51],"Fourier":[52],"modes":[53],"local":[55],"spatial":[56,71],"averages":[57],"over":[58],"finite":[59],"volume":[60],"elements.":[61],"Under":[62],"suitable":[63],"conditions":[64],"on":[65,118],"relaxation":[67],"(nudging)":[68],"parameter,":[69],"mesh":[72],"resolution,":[73],"step":[77],"between":[78,91],"successive":[79],"measurements,":[80,103],"we":[81],"obtain":[82],"an":[83,105],"asymptotic":[84],"estimate":[87],"difference":[90],"approximating":[93],"solution":[94,99],"unknown":[97],"reference":[98],"corresponding":[100],"appropriate":[106],"norm,":[107],"which":[108,116],"shows":[109],"exponential":[110],"convergence":[111],"up":[112],"term":[115],"depends":[117],"size":[120],"A":[124],"stationary":[125],"statistical":[126],"analysis":[127],"our":[129],"discrete":[130],"also":[135],"provided.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":8},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}