Some a priori error estimates with respect to H-theta norms, 0 <theta < 1, for the h-extension of the finite element method in tow dimensions

Tsamasphyros, G; Markolefas, S

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Markolefas, S	en
dc.date.accessioned	2014-03-01T01:54:47Z
dc.date.available	2014-03-01T01:54:47Z
dc.date.issued	2005	en
dc.identifier.issn	0168-9274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27465
dc.subject	finite elements	en
dc.subject	h-extensions	en
dc.subject	a priori error estimates	en
dc.subject	fractional order norms	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	RITZ-GALERKIN METHODS	en
dc.subject.other	P-VERSION	en
dc.subject.other	CONVERGENCE	en
dc.subject.other	SHARPNESS	en
dc.title	Some a priori error estimates with respect to H-theta norms, 0 <theta < 1, for the h-extension of the finite element method in tow dimensions	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	The error with respect to lower (fractional) order norms, \\*\\(theta), 0 < theta < 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 is an element of H1+delta-epsilon(Omega), For Allepsilon > 0, 0 < delta < 1), the optimal rate of convergence is recovered for theta > 1 - delta. Moreover, for 0 less than or equal to 1 - delta the deduced error upper bound has the same order as the classical error estimate with respect to L-2 norm (based upon the Aubin-Nitsche method). Finally, lower bound estimates of the form \\e(h)\\(theta) greater than or equal to C\\e(h)\\(2)(1), for some values of theta and positive definite unsymmetric bilinear functionals, are deduced. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	APPLIED NUMERICAL MATHEMATICS	en
dc.identifier.isi	ISI:000226566600007	en
dc.identifier.volume	52	en
dc.identifier.issue	4	en
dc.identifier.spage	449	en
dc.identifier.epage	458	en