Ferraz-Leite, S., Ortner, Christoph and Praetorius, Dirk (2008) Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators. Numerische Mathematik, Volume 116 (Number 2). pp. 291-316. doi:10.1007/s00211-010-0292-9 ISSN 0029-599X.

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Abstract

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Galerkin methods
Journal or Publication Title:	Numerische Mathematik
Publisher:	Springer
ISSN:	0029-599X
Official Date:	August 2008
Dates:	Date Event August 2008 Published
Volume:	Volume 116
Number:	Number 2
Number of Pages:	26
Page Range:	pp. 291-316
DOI:	10.1007/s00211-010-0292-9
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	22 December 2015
Date of first compliant Open Access:	22 December 2015
Funder:	Fonds zur Förderung der Wissenschaftlichen Forschung (Austria) (FWF)
Grant number:	W800-N05 (FWF), P21732 (FWF)

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