{"id":"https://openalex.org/W1988012040","doi":"https://doi.org/10.1137/060653834","title":"Maximum $L^2$\u2010Convergence Rates of the Crank\u2013Nicolson Scheme to the Stokes Initial Value Problem","display_name":"Maximum $L^2$\u2010Convergence Rates of the Crank\u2013Nicolson Scheme to the Stokes Initial Value Problem","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1988012040","doi":"https://doi.org/10.1137/060653834","mag":"1988012040"},"language":"en","primary_location":{"id":"doi:10.1137/060653834","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060653834","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/A5055595981","display_name":"Juergen Rodenkirchen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Juergen Rodenkirchen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055595981"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4485,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.58342719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"45","issue":"2","first_page":"484","last_page":"499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.998199999332428,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9979000091552734,"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":0.8899815678596497},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.6732946634292603},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6535711884498596},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.460226833820343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42707979679107666},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.41215047240257263},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41132816672325134},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.20660796761512756},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1308632493019104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11449670791625977}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8899815678596497},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.6732946634292603},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6535711884498596},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.460226833820343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42707979679107666},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.41215047240257263},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41132816672325134},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.20660796761512756},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1308632493019104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11449670791625977},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060653834","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060653834","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W15335618","https://openalex.org/W331343667","https://openalex.org/W370996200","https://openalex.org/W583893368","https://openalex.org/W621351040","https://openalex.org/W1467102747","https://openalex.org/W1527296550","https://openalex.org/W1533889494","https://openalex.org/W1546321017","https://openalex.org/W1575147392","https://openalex.org/W1595065160","https://openalex.org/W1598074861","https://openalex.org/W1963952659","https://openalex.org/W1985101615","https://openalex.org/W1986227787","https://openalex.org/W1990011930","https://openalex.org/W2005773176","https://openalex.org/W2033305412","https://openalex.org/W2043067292","https://openalex.org/W2043876702","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2055360045","https://openalex.org/W2064995425","https://openalex.org/W2090194109","https://openalex.org/W2101743932","https://openalex.org/W2121428337","https://openalex.org/W2798556646","https://openalex.org/W4231160115","https://openalex.org/W4245810802"],"related_works":["https://openalex.org/W4223970227","https://openalex.org/W4382021032","https://openalex.org/W1995356791","https://openalex.org/W3049665010","https://openalex.org/W940193414","https://openalex.org/W2773756540","https://openalex.org/W2026628742","https://openalex.org/W2375655024","https://openalex.org/W2463834842","https://openalex.org/W2939836502"],"abstract_inverted_index":{"Let":[0],"A":[1],"denote":[2],"the":[3,8,17,34,96,100,104],"Stokes":[4,19],"operator":[5],"and":[6,102,118],"$D_{A^{\\alpha}}$":[7],"domain":[9],"of":[10,40,89,99,106],"its":[11],"fractional":[12],"powers":[13],"$A^{\\alpha}$.":[14],"We":[15],"consider":[16],"homogeneous":[18],"initial":[20,24],"value":[21],"problem":[22],"with":[23,82,122],"data":[25,101],"$u(0)=u_{0}\\in":[26],"D_{A^{1+\\varepsilon}}$,":[27],"$\\varepsilon":[28,36,48],"\\in":[29,37],"(0,1)$.":[30],"For":[31],"Stokes\u2010like":[32],"equations":[33],"range":[35],"(0,\\frac{1}{4})$":[38],"is":[39,93],"special":[41],"interest,":[42],"as":[43,108],"any":[44,67],"solution":[45,69],"derived":[46,115],"from":[47],"\\ge":[49],"\\frac{1}{4}$":[50],"would":[51],"necessarily":[52],"have":[53],"to":[54],"satisfy":[55],"an":[56],"additional,":[57],"in":[58,73],"practice":[59],"unverifiable":[60],"compatibility":[61],"condition":[62],"at":[63],"time":[64,74,79],"$t=0$.":[65],"Approximating":[66],"strong":[68],"$u\\in":[70],"C^{0}([0,\\infty":[71],"),D_{A^{1+\\varepsilon}})$":[72],"direction":[75],"on":[76],"a":[77,83,123],"finite":[78],"interval":[80],"$[0,T]$":[81],"Crank\u2013Nicolson":[84],"scheme,":[85],"we":[86],"show":[87],"convergence":[88],"order":[90],"$O(\\frac{\\tau^{2}}{t^{1-\\varepsilon}})$":[91],"which":[92],"maximal":[94],"for":[95],"assumed":[97],"regularity":[98,107],"reflects":[103],"loss":[105],"$t\\rightarrow":[109],"0$.":[110],"The":[111],"error":[112],"estimates":[113],"are":[114],"by":[116],"energy":[117],"semigroup":[119],"methods":[120],"combined":[121],"parabolic":[124],"duality":[125],"argument.":[126]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
