Some a priori error estimates with respect to Hθ norms, 0&lt;θ&lt;1, for the h-extension of the finite element method in two dimensions

Tsamasphyros, G; Markolefas, S

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Markolefas, S	en
dc.date.accessioned	2014-03-01T01:23:06Z
dc.date.available	2014-03-01T01:23:06Z
dc.date.issued	2005	en
dc.identifier.issn	01689274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16812
dc.subject	A priori error estimates	en
dc.subject	Finite elements	en
dc.subject	Fractional order norms	en
dc.subject	h-extension	en
dc.subject.other	A priori error estimates	en
dc.subject.other	Finite elements	en
dc.subject.other	Fractional order norms	en
dc.subject.other	H-extension	en
dc.subject.other	Error detection	en
dc.subject.other	Finite element method	en
dc.subject.other	Functions	en
dc.subject.other	Interpolation	en
dc.subject.other	Mathematical models	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Problem solving	en
dc.subject.other	Hydrogen	en
dc.title	Some a priori error estimates with respect to Hθ norms, 0<θ<1, for the h-extension of the finite element method in two dimensions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.apnum.2004.07.005	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.apnum.2004.07.005	en
heal.publicationDate	2005	en
heal.abstract	The error with respect to lower (fractional) order norms, ∥*∥θ, 0<θ<1, for the h-extension of the finite element method in 2-D, is studied and some new improved error estimates are deduced. In particular, it is shown that in polygonal domains, where the singularities dominate the regularity of the exact solution (e.g., u∈H1+δ-ε(Ω),∀ε>0,0<δ<1), the optimal rate of convergence is recovered for θ>1-δ. Moreover, for θ≤1-δ the deduced error upper bound has the same order as the classical error estimate with respect to L2 norm (based upon the Aubin-Nitsche method). Finally, lower bound estimates of the form ∥eh∥θ≥ C∥eh∥12, for some values of θ and positive definite unsymmetric bilinear functionals, are deduced. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.	en
heal.journalName	Applied Numerical Mathematics	en
dc.identifier.doi	10.1016/j.apnum.2004.07.005	en
dc.identifier.volume	52	en
dc.identifier.issue	4	en
dc.identifier.spage	449	en
dc.identifier.epage	458	en