{"id":"https://openalex.org/W1971251312","doi":"https://doi.org/10.1137/050634335","title":"Semi\u2010implicit Euler Scheme for Generalized Newtonian Fluids","display_name":"Semi\u2010implicit Euler Scheme for Generalized Newtonian Fluids","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1971251312","doi":"https://doi.org/10.1137/050634335","mag":"1971251312"},"language":"en","primary_location":{"id":"doi:10.1137/050634335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050634335","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/A5010484841","display_name":"Lars Diening","orcid":"https://orcid.org/0000-0002-0523-3079"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lars Diening","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046668672","display_name":"Andreas Prohl","orcid":"https://orcid.org/0000-0003-4523-9536"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas Prohl","raw_affiliation_strings":[],"affiliations":[]},{"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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael R\u016f\u017ei\u010dka","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010484841"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8201,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.92464255,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"3","first_page":"1172","last_page":"1190"},"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":0.9991999864578247,"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":0.9991999864578247,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8450697064399719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7735170722007751},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5259609222412109},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5074118971824646},{"id":"https://openalex.org/keywords/newtonian-fluid","display_name":"Newtonian fluid","score":0.49938535690307617},{"id":"https://openalex.org/keywords/non-newtonian-fluid","display_name":"Non-Newtonian fluid","score":0.49603375792503357},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4539390504360199},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42544251680374146},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35272306203842163},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.340897798538208},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1275673508644104},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.09625959396362305}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8450697064399719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7735170722007751},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5259609222412109},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5074118971824646},{"id":"https://openalex.org/C294558","wikidata":"https://www.wikidata.org/wiki/Q366968","display_name":"Newtonian fluid","level":2,"score":0.49938535690307617},{"id":"https://openalex.org/C84403224","wikidata":"https://www.wikidata.org/wiki/Q860589","display_name":"Non-Newtonian fluid","level":2,"score":0.49603375792503357},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4539390504360199},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42544251680374146},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35272306203842163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.340897798538208},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1275673508644104},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.09625959396362305},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050634335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050634335","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:10.1.1.494.8629","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.494.8629","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ethz.ch/research/groups/fim/preprints/2005/prohl5.pdf","raw_type":"text"},{"id":"pmh:oai:pub.librecat.org:2913536","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2913536","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":"Diening L, Prohl A, R\u016f\u017ei\u010dka M. Semi-implicit Euler scheme for generalized Newtonian fluids. <em>SIAM Journal on Numerical Analysis</em>. 2006;44(3):1172-1190.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W172070285","https://openalex.org/W1601998939","https://openalex.org/W1602259421","https://openalex.org/W1995848276","https://openalex.org/W2009802721","https://openalex.org/W2033305412","https://openalex.org/W2086208233","https://openalex.org/W2112166131","https://openalex.org/W2126393529","https://openalex.org/W2324799522","https://openalex.org/W2476594125","https://openalex.org/W3091814460"],"related_works":["https://openalex.org/W1992244398","https://openalex.org/W3005204046","https://openalex.org/W2911367846","https://openalex.org/W2104831383","https://openalex.org/W2037834696","https://openalex.org/W2096756136","https://openalex.org/W1697484951","https://openalex.org/W4224324152","https://openalex.org/W2021837978","https://openalex.org/W2045476869"],"abstract_inverted_index":{"Rheological":[0],"behavior":[1],"of":[2,40,88],"certain":[3],"non\u2010Newtonian":[4],"fluids":[5],"in":[6,75,101,104],"engineering":[7],"sciences":[8],"is":[9,126,144],"often":[10],"modeled":[11],"by":[12],"power":[13],"law":[14],"ansatzes":[15],"with":[16],"$p":[17,136],"\\leq":[18],"2$.":[19],"So":[20],"far,":[21],"existing":[22],"numerical":[23],"analysis":[24,69],"for":[25,43,70,82],"local":[26],"strong":[27],"solutions":[28],"studies":[29],"a":[30,66,121,145],"fully":[31],"implicit":[32],"time":[33,123],"discretization":[34,124],"and":[35,49,79,93,98,107,128],"find":[36],"only":[37],"restricted":[38],"ranges":[39],"admissible":[41],"p\u2019s":[42,72],"corresponding":[44,67],"error":[45,68,129],"estimates":[46,130],"[A.":[47],"Prohl":[48],"M.":[50,99],"R\u016f\u017ei\u010dka,":[51,100],"SIAM":[52],"J.":[53],"Numer.":[54],"Anal.,":[55],"39":[56],"(2001),":[57],"pp.":[58,115],"214\u2013249];":[59],"different":[60],"nonlinear":[61],"stabilization":[62],"strategies":[63],"which":[64],"allow":[65],"smaller":[71],"are":[73],"examined":[74],"[L.":[76,94],"Diening,":[77,95],"Theoretical":[78],"Numerical":[80],"Results":[81],"Electrorheological":[83],"Fluids,":[84],"Ph.D.":[85],"thesis,":[86],"University":[87],"Freiburg,":[89,90],"Germany,":[91],"2002]":[92],"A.":[96],"Prohl,":[97],"Nonlinear":[102],"Problems":[103],"Mathematical":[105],"Physics":[106],"Related":[108],"Topics,":[109],"II,":[110],"Kluwer/Plenum,":[111],"New":[112],"York,":[113],"2002,":[114],"89\u2013118].":[116],"In":[117],"the":[118,133],"present":[119],"paper,":[120],"semi\u2010implicit":[122],"scheme":[125],"proposed,":[127],"apply":[131],"to":[132],"extended":[134],"range":[135],"\\in":[137],"(\\frac{3}{2}":[138],",2]$.":[139],"The":[140],"key":[141],"analytical":[142],"tool":[143],"new":[146],"Gronwall\u2010type":[147],"inequality.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}