{"id":"https://openalex.org/W1994964641","doi":"https://doi.org/10.1137/s0036142903428967","title":"On a Linearized Backward Euler Method for the Equations of Motion of Oldroyd Fluids of Order One","display_name":"On a Linearized Backward Euler Method for the Equations of Motion of Oldroyd Fluids of Order One","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1994964641","doi":"https://doi.org/10.1137/s0036142903428967","mag":"1994964641"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903428967","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903428967","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/A5034307785","display_name":"Amiya K. Pani","orcid":"https://orcid.org/0000-0002-0477-9272"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Amiya K. Pani","raw_affiliation_strings":["Indian Inst. of Technology, Bombay"],"affiliations":[{"raw_affiliation_string":"Indian Inst. of Technology, Bombay","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100603554","display_name":"Jin Yuan","orcid":"https://orcid.org/0000-0002-5803-6626"},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jin Yun Yuan","raw_affiliation_strings":["Federal University of Paran\u00e0"],"affiliations":[{"raw_affiliation_string":"Federal University of Paran\u00e0","institution_ids":["https://openalex.org/I52418104"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089902495","display_name":"Pedro D. Dam\u00e1zio","orcid":"https://orcid.org/0000-0002-7575-4523"},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Pedro D. Dam\u00e1zio","raw_affiliation_strings":["Federal University of Paran\u00e0"],"affiliations":[{"raw_affiliation_string":"Federal University of Paran\u00e0","institution_ids":["https://openalex.org/I52418104"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034307785"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.8438,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.73079396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"2","first_page":"804","last_page":"825"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9962999820709229,"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":0.8177613019943237},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7252789735794067},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.7154119610786438},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.6049412488937378},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5809255838394165},{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.5807658433914185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.576106071472168},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5541113615036011},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.5109695196151733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49320000410079956},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.49109530448913574},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.4639320969581604},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4581628441810608},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4113844931125641},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14140984416007996},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11248883605003357}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8177613019943237},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7252789735794067},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.7154119610786438},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.6049412488937378},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5809255838394165},{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.5807658433914185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.576106071472168},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5541113615036011},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.5109695196151733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.49109530448913574},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.4639320969581604},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4581628441810608},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4113844931125641},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14140984416007996},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11248883605003357},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142903428967","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903428967","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:dsapce.library.iitb.ac.in:10054/11977","is_oa":false,"landing_page_url":"http://doi.org/10.1137/S0036142903428967","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dspace.library.iitb.ac.in:10054/11977","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/xmlui/handle/10054/11977","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W69614788","https://openalex.org/W649861147","https://openalex.org/W1518050517","https://openalex.org/W1964442237","https://openalex.org/W1983119685","https://openalex.org/W1987049901","https://openalex.org/W1993821520","https://openalex.org/W2003377329","https://openalex.org/W2021197747","https://openalex.org/W2026110563","https://openalex.org/W2033305412","https://openalex.org/W2038129768","https://openalex.org/W2043235005","https://openalex.org/W2043876702","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2053384289","https://openalex.org/W2061881346","https://openalex.org/W2073204000","https://openalex.org/W2076582418","https://openalex.org/W2082621526","https://openalex.org/W2084261042","https://openalex.org/W2126672608","https://openalex.org/W2130690746","https://openalex.org/W2154615457","https://openalex.org/W2222425717","https://openalex.org/W2477040106","https://openalex.org/W2568327493","https://openalex.org/W2591048038","https://openalex.org/W2894951100","https://openalex.org/W3042562017","https://openalex.org/W3217405257","https://openalex.org/W4231160115","https://openalex.org/W4242273588","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2349121885","https://openalex.org/W1674877062","https://openalex.org/W2009711572","https://openalex.org/W2189596786","https://openalex.org/W2039299714","https://openalex.org/W2417495913","https://openalex.org/W2079547538","https://openalex.org/W2001126463","https://openalex.org/W1965897387"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,25,57],"linearized":[4],"backward":[5],"Euler":[6],"method":[7],"is":[8],"discussed":[9],"for":[10,30,45,67,76],"the":[11,17,31,38,41,46,51,68,69],"equations":[12],"of":[13,20],"motion":[14],"arising":[15],"in":[16,61],"Oldroyd":[18],"model":[19],"viscoelastic":[21],"fluids.":[22],"Some":[23],"new":[24],"priori":[26,58],"bounds":[27],"are":[28,54,65,73],"obtained":[29],"solution":[32],"under":[33],"realistically":[34],"assumed":[35],"conditions":[36],"on":[37],"data.":[39],"Further,":[40],"exponential":[42],"decay":[43],"properties":[44],"exact":[47],"as":[48,50],"well":[49],"discrete":[52,70],"solutions":[53],"established.":[55],"Finally,":[56],"error":[59],"estimates":[60],"$\\bH^1$":[62],"and":[63],"$\\bL^2$-norms":[64],"derived":[66],"problem":[71],"which":[72],"valid":[74],"uniformly":[75],"all":[77],"time":[78],"$t>0$.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}