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https://doi.org/10.21256/zhaw-22705| Publication type: | Article in scientific journal |
| Type of review: | Peer review (publication) |
| Title: | Estimates of the modeling error generated by homogenization of an elliptic boundary value problem |
| Authors: | Repin, Sergey Samrowski, Tatiana Sauter, Stefan |
| et. al: | No |
| DOI: | 10.1515/jnma-2014-1002 10.21256/zhaw-22705 |
| Published in: | Journal of Numerical Mathematics |
| Volume(Issue): | 24 |
| Issue: | 1 |
| Page(s): | 1 |
| Pages to: | 15 |
| Issue Date: | 2016 |
| Publisher / Ed. Institution: | De Gruyter |
| ISSN: | 1569-3953 1570-2820 |
| Language: | English |
| Subjects: | Periodic structure; Homogenization; Elliptic boundary value problem; A posteriori error estimate; Modeling error |
| Subject (DDC): | 510: Mathematics |
| 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. |
| Further description: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/22705 |
| Fulltext version: | Published version |
| License (according to publishing contract): | Licence according to publishing contract |
| Departement: | School of Engineering |
| Organisational Unit: | Institute of Applied Mathematics and Physics (IAMP) |
| Appears in collections: | Publikationen School of Engineering |
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| 2016_Repin-etal_Modeling-error-homogenization-elliptic-boundary-value-problem.pdf | 310.05 kB | Adobe PDF |  View/Open |
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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
Repin, S., Samrowski, T. and Sauter, S. (2016) ‘Estimates of the modeling error generated by homogenization of an elliptic boundary value problem’, Journal of Numerical Mathematics, 24(1), pp. 1–15. Available at: https://doi.org/10.1515/jnma-2014-1002.
S. Repin, T. Samrowski, and S. Sauter, “Estimates of the modeling error generated by homogenization of an elliptic boundary value problem,” Journal of Numerical Mathematics, vol. 24, no. 1, pp. 1–15, 2016, doi: 10.1515/jnma-2014-1002.
REPIN, Sergey, Tatiana SAMROWSKI und Stefan SAUTER, 2016. Estimates of the modeling error generated by homogenization of an elliptic boundary value problem. Journal of Numerical Mathematics. 2016. Bd. 24, Nr. 1, S. 1–15. DOI 10.1515/jnma-2014-1002
Repin, Sergey, Tatiana Samrowski, and Stefan Sauter. 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.
Repin, Sergey, et al. “Estimates of the Modeling Error Generated by Homogenization of an Elliptic Boundary Value Problem.” Journal of Numerical Mathematics, vol. 24, no. 1, 2016, pp. 1–15, https://doi.org/10.1515/jnma-2014-1002.
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