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Please use this identifier to cite or link to this item: https://olympias.lib.uoi.gr/jspui/handle/123456789/10890
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dc.contributor.authorAkrivis, G.en
dc.contributor.authorMakridakis, C.en
dc.contributor.authorNochetto, R. H.en
dc.date.accessioned2015-11-24T17:01:13Z-
dc.date.available2015-11-24T17:01:13Z-
dc.identifier.issn0025-5718-
dc.identifier.urihttps://olympias.lib.uoi.gr/jspui/handle/123456789/10890-
dc.rightsDefault Licence-
dc.subjectparabolic equationsen
dc.subjectcrank-nicolson methoden
dc.subjectcrank-nicolson galerkin methoden
dc.subjectcrank-nicolson reconstructionen
dc.subjectcrank-nicolson-galerkin reconstructionen
dc.subjecta posteriori error analysisen
dc.subjectfinite-element methodsen
dc.subjectschrodinger-equationen
dc.subjectheat-equationen
dc.subjecttimeen
dc.subjectdiscretizationsen
dc.subjectspaceen
dc.titleA posteriori error estimates for the Crank-Nicolson method for parabolic equationsen
heal.typejournalArticle-
heal.type.enJournal articleen
heal.type.elΆρθρο Περιοδικούel
heal.languageen-
heal.accesscampus-
heal.recordProviderΠανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικήςel
heal.publicationDate2006-
heal.abstractWe derive optimal order a posteriori error estimates for time discretizations by both the Crank-Nicolson and the Crank-Nicolson-Galerkin methods for linear and nonlinear parabolic equations. We examine both smooth and rough initial data. Our basic tool for deriving a posteriori estimates are second-order Crank-Nicolson reconstructions of the piecewise linear approximate solutions. These functions satisfy two fundamental properties: (i) they are explicitly computable and thus their difference to the numerical solution is controlled a posteriori, and (ii) they lead to optimal order residuals as well as to appropriate pointwise representations of the error equation of the same form as the underlying evolution equation. The resulting estimators are shown to be of optimal order by deriving upper and lower bounds for them depending only on the discretization parameters and the data of our problem. As a consequence we provide alternative proofs for known a priori rates of convergence for the Crank-Nicolson method.en
heal.journalNameMathematics of Computationen
heal.journalTypepeer reviewed-
heal.fullTextAvailabilityTRUE-
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