{"id":"https://openalex.org/W2065369165","doi":"https://doi.org/10.1137/080720024","title":"Optimal Error Estimates for a Semi-Implicit Euler Scheme for Incompressible Fluids with Shear Dependent Viscosities","display_name":"Optimal Error Estimates for a Semi-Implicit Euler Scheme for Incompressible Fluids with Shear Dependent Viscosities","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2065369165","doi":"https://doi.org/10.1137/080720024","mag":"2065369165"},"language":"en","primary_location":{"id":"doi:10.1137/080720024","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080720024","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5069567984","display_name":"Luigi C. Berselli","orcid":"https://orcid.org/0000-0001-6208-9934"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luigi C. Berselli","raw_affiliation_strings":["berselli@dma.unipi.it#TAB#"],"affiliations":[{"raw_affiliation_string":"berselli@dma.unipi.it#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010484841","display_name":"Lars Diening","orcid":"https://orcid.org/0000-0002-0523-3079"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lars Diening","raw_affiliation_strings":["diening@mathematik.uni-freiburg.de and rose@mathematik.uni-freiburg.de#TAB#"],"affiliations":[{"raw_affiliation_string":"diening@mathematik.uni-freiburg.de and rose@mathematik.uni-freiburg.de#TAB#","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027944157","display_name":"Michael R\u016f\u017ei\u010dka","orcid":"https://orcid.org/0000-0001-8497-1864"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael R\u016f\u017ei\u010dka","raw_affiliation_strings":["Albert-Ludwigs-University of Freiburg"],"affiliations":[{"raw_affiliation_string":"Albert-Ludwigs-University of Freiburg","institution_ids":["https://openalex.org/I161046081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069567984"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.14014712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"47","issue":"3","first_page":"2177","last_page":"2202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9952999949455261,"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/mathematics","display_name":"Mathematics","score":0.7948837280273438},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.7498797178268433},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6854584217071533},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6095318794250488},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5001962184906006},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.49301406741142273},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.48503655195236206},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.45342397689819336},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44237416982650757},{"id":"https://openalex.org/keywords/rheology","display_name":"Rheology","score":0.43928804993629456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40680399537086487},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16660678386688232},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.15660390257835388},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1115942895412445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1008366048336029},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08412262797355652}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7948837280273438},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.7498797178268433},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6854584217071533},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6095318794250488},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5001962184906006},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.49301406741142273},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.48503655195236206},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.45342397689819336},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44237416982650757},{"id":"https://openalex.org/C200990466","wikidata":"https://www.wikidata.org/wiki/Q271707","display_name":"Rheology","level":2,"score":0.43928804993629456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40680399537086487},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16660678386688232},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.15660390257835388},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1115942895412445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1008366048336029},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08412262797355652},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/080720024","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080720024","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.503.3386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.3386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://aam.mathematik.uni-freiburg.de/IAM/homepages/diening/archive/paper_numeric_luigi_lm.pdf","raw_type":"text"},{"id":"pmh:oai:arpi.unipi.it:11568/127135","is_oa":false,"landing_page_url":"https://epubs.siam.org/doi/10.1137/080720024","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pub.librecat.org:2913524","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2913524","pdf_url":null,"source":{"id":"https://openalex.org/S4306401671","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Berselli LC, Diening L, R\u016f\u017ei\u010dka M. Optimal error estimates for a semi-implicit Euler scheme for incompressible fluids with shear dependent viscosities. <em>SIAM Journal on Numerical Analysis</em>. 2009;47(3):2177-2202.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W47332096","https://openalex.org/W172070285","https://openalex.org/W579813348","https://openalex.org/W1212181859","https://openalex.org/W1483870296","https://openalex.org/W1485957485","https://openalex.org/W1556837715","https://openalex.org/W1892834595","https://openalex.org/W1963952659","https://openalex.org/W1964688360","https://openalex.org/W1965234251","https://openalex.org/W1967011851","https://openalex.org/W1971251312","https://openalex.org/W1995848276","https://openalex.org/W2009802721","https://openalex.org/W2012423916","https://openalex.org/W2014595925","https://openalex.org/W2033305412","https://openalex.org/W2038490905","https://openalex.org/W2043067292","https://openalex.org/W2043267610","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2052811761","https://openalex.org/W2054391632","https://openalex.org/W2061988259","https://openalex.org/W2072741826","https://openalex.org/W2075872548","https://openalex.org/W2082621526","https://openalex.org/W2086208233","https://openalex.org/W2089773056","https://openalex.org/W2101743932","https://openalex.org/W2112166131","https://openalex.org/W2122543191","https://openalex.org/W2126393529","https://openalex.org/W2146785120","https://openalex.org/W2149921380","https://openalex.org/W2153317684","https://openalex.org/W2168795429","https://openalex.org/W2240493994","https://openalex.org/W2324799522","https://openalex.org/W2477040106","https://openalex.org/W2505105003"],"related_works":["https://openalex.org/W4381954624","https://openalex.org/W3162423291","https://openalex.org/W2111739703","https://openalex.org/W1697484951","https://openalex.org/W2911367846","https://openalex.org/W4297084911","https://openalex.org/W2021837978","https://openalex.org/W2085547843","https://openalex.org/W2052335704","https://openalex.org/W3005204046"],"abstract_inverted_index":{"Certain":[0],"rheological":[1],"behaviors":[2],"of":[3,60,85,93,96],"fluids":[4,27],"in":[5,49],"engineering":[6],"sciences":[7],"are":[8,76,100],"modeled":[9],"by":[10],"power":[11],"law":[12],"ansatz":[13],"with":[14,78],"$p\\in(1,2]$.":[15],"In":[16],"the":[17,34,42,50,54,61,72,81,86,94,97],"present":[18],"paper":[19],"a":[20],"semi-implicit":[21],"time":[22,43],"discretization":[23],"scheme":[24],"for":[25,57],"such":[26],"is":[28,33,41,66],"proposed.":[29],"The":[30,74],"main":[31],"result":[32],"optimal":[35],"$\\mathcal{O}(k)$":[36],"error":[37],"estimate,":[38],"where":[39],"k":[40],"step":[44],"size.":[45],"Our":[46],"results":[47],"hold":[48],"range":[51],"$p\\in(3/2,2]$":[52],"(in":[53],"three-dimensional":[55],"setting)":[56],"strong":[58],"solutions":[59],"continuous":[62],"problem,":[63],"whose":[64],"existence":[65],"guaranteed":[67],"under":[68],"appropriate":[69],"assumptions":[70],"on":[71],"data.":[73],"estimates":[75],"uniform":[77],"respect":[79],"to":[80],"degeneracy":[82],"parameter":[83],"$\\delta\\in[0,\\delta_0]$":[84],"extra":[87],"stress":[88],"tensor.":[89],"Additional":[90],"regularity":[91],"properties":[92],"solution":[95],"discrete":[98],"problem":[99],"proved.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}