A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods

A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the t...

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Main Authors: Hakima Benlarbi, Ahmed-Salah Chibi
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/947085
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author Hakima Benlarbi
Ahmed-Salah Chibi
author_facet Hakima Benlarbi
Ahmed-Salah Chibi
author_sort Hakima Benlarbi
collection DOAJ
description A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.
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institution Kabale University
issn 1110-757X
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publishDate 2012-01-01
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series Journal of Applied Mathematics
spelling doaj-art-fe80386655b1470382e760945f0ca2c32025-08-20T03:25:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/947085947085A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition MethodsHakima Benlarbi0Ahmed-Salah Chibi1Department of Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, AlgeriaDepartment of Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, AlgeriaA posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.http://dx.doi.org/10.1155/2012/947085
spellingShingle Hakima Benlarbi
Ahmed-Salah Chibi
A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
Journal of Applied Mathematics
title A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
title_full A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
title_fullStr A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
title_full_unstemmed A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
title_short A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
title_sort posteriori error estimates for the generalized overlapping domain decomposition methods
url http://dx.doi.org/10.1155/2012/947085
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AT ahmedsalahchibi aposteriorierrorestimatesforthegeneralizedoverlappingdomaindecompositionmethods
AT hakimabenlarbi posteriorierrorestimatesforthegeneralizedoverlappingdomaindecompositionmethods
AT ahmedsalahchibi posteriorierrorestimatesforthegeneralizedoverlappingdomaindecompositionmethods