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Estimates of the modeling error generated by homogenization of an elliptic boundary value problem


Repin, Sergey I; Samrowski, Tatiana S; Sauter, Stefan A (2016). Estimates of the modeling error generated by homogenization of an elliptic boundary value problem. Journal of Numerical Mathematics, 24(1):1-15.

Abstract

In this paper, we derive a posteriori bounds of the difference between the exact solution of an elliptic boundary value problem with periodic coefficients and an abridged model, which follows from the homogenization theory. The difference is measured in terms of the energy norm of the basic problem and also in the combined primal–dual norm. Using the technique of functional type a posteriori error estimates, we obtain two-sided bounds of the modelling error, which depends only on known data and the solution of the homogenized problem. It is proved that the majorant with properly chosen arguments possesses the same convergence rate, which was established for the true error. Numerical tests confirm the efficiency of the estimates.

Abstract

In this paper, we derive a posteriori bounds of the difference between the exact solution of an elliptic boundary value problem with periodic coefficients and an abridged model, which follows from the homogenization theory. The difference is measured in terms of the energy norm of the basic problem and also in the combined primal–dual norm. Using the technique of functional type a posteriori error estimates, we obtain two-sided bounds of the modelling error, which depends only on known data and the solution of the homogenized problem. It is proved that the majorant with properly chosen arguments possesses the same convergence rate, which was established for the true error. Numerical tests confirm the efficiency of the estimates.

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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:March 2016
Deposited On:02 Feb 2017 08:31
Last Modified:02 Feb 2018 11:58
Publisher:Walter de Gruyter GmbH
ISSN:1570-2820
OA Status:Green
Publisher DOI:https://doi.org/10.1515/jnma-2014-1002

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