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A posteriori estimation of dimension reduction errors for elliptic problems on thin domains


Repin, S; Sauter, S; Smolianski, A (2004). A posteriori estimation of dimension reduction errors for elliptic problems on thin domains. SIAM Journal on Numerical Analysis, 42(4):1435-1451.

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. For the energy norm of the error of the zero-order dimension reduction method, the proposed estimator is shown to always provide a guaranteed upper bound. In the case when the original domain has constant thickness (but, possibly, nonplane upper and lower faces), the estimator demonstrates the optimal convergence rate as the thickness tends to zero. It is also flexible enough to successfully cope with infinitely growing right-hand sides in the equation when the domain thickness tends to zero. The numerical tests indicate the efficiency of the estimator and its ability to accurately represent the local error distribution needed for an adaptive improvement of the reduced model.

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. For the energy norm of the error of the zero-order dimension reduction method, the proposed estimator is shown to always provide a guaranteed upper bound. In the case when the original domain has constant thickness (but, possibly, nonplane upper and lower faces), the estimator demonstrates the optimal convergence rate as the thickness tends to zero. It is also flexible enough to successfully cope with infinitely growing right-hand sides in the equation when the domain thickness tends to zero. The numerical tests indicate the efficiency of the estimator and its ability to accurately represent the local error distribution needed for an adaptive improvement of the reduced model.

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11 citations in Web of Science®
8 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2004
Deposited On:27 Feb 2010 00:23
Last Modified:05 Apr 2016 13:24
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
Additional Information:Copyright © 2004, Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/030602381
Permanent URL: https://doi.org/10.5167/uzh-21822

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