Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
Abstract
In this paper, we derive a posteriori bounds of the di erence between the exact solution of an elliptic
boundary value problem with periodic coe cients and an abridged model, which follows from the homogenization
theory. The di erence 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 modeling 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 con rm the effi ciency of the estimates.
Main Authors
Format
Articles
Research article
Published
2016
Series
Subjects
Publication in research information system
Publisher
Walter de Gruyter GmbH & Co. KG
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201604072025Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1570-2820
DOI
https://doi.org/10.1515/jnma-2014-1002
Language
English
Published in
Journal of Numerical Mathematics
Citation
- Repin, S., Samrowski, T., & Sauter, S. (2016). Estimates of the modeling error generated by homogenization of an elliptic boundary value problem. Journal of Numerical Mathematics, 24(1), 1-15. https://doi.org/10.1515/jnma-2014-1002
License
Copyright© Walter de Gruyter GmbH, 2016. Published in this repository with the kind permission of the publisher.