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Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators
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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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Official URL: http://dx.doi.org/10.1007/s00211-010-0292-9
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 | ||||
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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: |
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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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