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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.

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
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISBN:3-540-21460-7
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1056.65105
Permanent URL: https://doi.org/10.5167/uzh-21819

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