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A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions


Repin, S; Sauter, S; Smolianski, A (2004). A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Journal of Computational and Applied Mathematics, 164/16:601-612.

Abstract

The present work is devoted to the a posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Using the duality technique we derive a reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1, independently of the discretization method chosen. Only two global constants appear in the definition of the estimator; both constants depend solely on the domain geometry, and the estimator is quite nonsensitive to the error in the constants evaluation. It is also shown how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.

Abstract

The present work is devoted to the a posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Using the duality technique we derive a reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1, independently of the discretization method chosen. Only two global constants appear in the definition of the estimator; both constants depend solely on the domain geometry, and the estimator is quite nonsensitive to the error in the constants evaluation. It is also shown how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.

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Additional indexing

Other titles:Proceedings of the 10th International Congress on Computational and Applied Mathematics
Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Mixed Dirichlet/Neumann boundary conditions; A posteriori error estimator; Reliability; Efficiency; Local error distribution
Language:English
Date:1 March 2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Elsevier
ISSN:0377-0427
Additional Information:Copyright © 2003 Published by Elsevier Science B.V.
Publisher DOI:https://doi.org/10.1016/S0377-0427(03)00491-6
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1038.65114

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