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https://doi.org/10.21256/zhaw-29622| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Combined error estimates in the case of dimension reduction |
| Autor/-in: | Samrowski, Tatiana |
| et. al: | No |
| DOI: | 10.1515/cmam-2013-0024 10.21256/zhaw-29622 |
| Erschienen in: | Computational Methods in Applied Mathematics |
| Band(Heft): | 14 |
| Heft: | 1 |
| Seite(n): | 113 |
| Seiten bis: | 134 |
| Erscheinungsdatum: | 2014 |
| Verlag / Hrsg. Institution: | De Gruyter |
| ISSN: | 1609-4840 1609-9389 |
| Sprache: | Englisch |
| Schlagwörter: | Modeling error; Dimension reduction; Thin domain; A posteriori error estimate |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | We consider the stationary reaction-diffusion problem in a domain Ω⊂ℝ3 having the size along one coordinate direction essentially smaller than along the others. By an energy type argumentation, different simplified models of lower dimension can be deduced and solved numerically. For these models, we derive a guaranteed upper bound of the difference between the exact solution of the original problem and a three-dimensional reconstruction generated by the solution of a dimensionally reduced problem. This estimate of the total error is determined as the sum of discretization and modeling errors, which are both explicit and computable. The corresponding discretization errors are estimated by a posteriori estimates of the functional type. Modeling error majorants are also explicitly evaluated. Hence, a numerical strategy based on the balancing modeling and discretization errors can be derived in order to provide an economical way of getting an approximate solution with an a priori given accuracy. Numerical tests are presented and discussed. |
| Weitere Angaben: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/29622 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | Lizenz gemäss Verlagsvertrag |
| Departement: | School of Engineering |
| Organisationseinheit: | Institut für Angewandte Mathematik und Physik (IAMP) |
| Enthalten in den Sammlungen: | Publikationen School of Engineering |
Dateien zu dieser Ressource:
| Datei | Beschreibung | Größe | Format | |
|---|---|---|---|---|
| 2014_Samrowski_Combined-error-estimates-dimension-reduction.pdf | 394.48 kB | Adobe PDF |  Öffnen/Anzeigen |
Zur Langanzeige
Samrowski, T. (2014). Combined error estimates in the case of dimension reduction. Computational Methods in Applied Mathematics, 14(1), 113–134. https://doi.org/10.1515/cmam-2013-0024
Samrowski, T. (2014) ‘Combined error estimates in the case of dimension reduction’, Computational Methods in Applied Mathematics, 14(1), pp. 113–134. Available at: https://doi.org/10.1515/cmam-2013-0024.
T. Samrowski, “Combined error estimates in the case of dimension reduction,” Computational Methods in Applied Mathematics, vol. 14, no. 1, pp. 113–134, 2014, doi: 10.1515/cmam-2013-0024.
SAMROWSKI, Tatiana, 2014. Combined error estimates in the case of dimension reduction. Computational Methods in Applied Mathematics. 2014. Bd. 14, Nr. 1, S. 113–134. DOI 10.1515/cmam-2013-0024
Samrowski, Tatiana. 2014. “Combined Error Estimates in the Case of Dimension Reduction.” Computational Methods in Applied Mathematics 14 (1): 113–34. https://doi.org/10.1515/cmam-2013-0024.
Samrowski, Tatiana. “Combined Error Estimates in the Case of Dimension Reduction.” Computational Methods in Applied Mathematics, vol. 14, no. 1, 2014, pp. 113–34, https://doi.org/10.1515/cmam-2013-0024.
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