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A posteriori estimation of dimension reduction errors


Repin, S; Sauter, S; Smolianski, A (2004). A posteriori estimation of dimension reduction errors. In: Feistauer, M. Numerical mathematics and advanced applications. Berlin: Springer, 716-725.

Abstract

A new a posteriori error estimator is presented for the verification of the dimensionally reduced models stemming from the elliptic problems on thin domains. The original problem is considered in a general setting, without any specific assumptions on the domain geometry, coefficients and the right-hand sides. The estimator provides a guaranteed upper bound for the modelling error in the energy norm, exhibits the optimal convergence rate as the domain thickness tends to zero and accurately indicates the local error distribution.

Abstract

A new a posteriori error estimator is presented for the verification of the dimensionally reduced models stemming from the elliptic problems on thin domains. The original problem is considered in a general setting, without any specific assumptions on the domain geometry, coefficients and the right-hand sides. The estimator provides a guaranteed upper bound for the modelling error in the energy norm, exhibits the optimal convergence rate as the domain thickness tends to zero and accurately indicates the local error distribution.

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Additional indexing

Other titles:Proceedings of the 5th European Conference (ENUMATH 2003) held in Prague, August 18–22, 2003
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Numerical Analysis
Physical Sciences > Computational Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:29 Jul 2020 19:40
Publisher:Springer
ISBN:3-540-21460-7
OA Status:Green
Publisher DOI:https://doi.org/10.1137/030602381
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1056.65105

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