Combined error estimates in the case of dimension reduction

Samrowski, Tatiana

doi:10.1515/cmam-2013-0024

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-29622

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Combined error estimates in the case of dimension reduction
Authors:	Samrowski, Tatiana
et. al:	No
DOI:	10.1515/cmam-2013-0024 10.21256/zhaw-29622
Published in:	Computational Methods in Applied Mathematics
Volume(Issue):	14
Issue:	1
Page(s):	113
Pages to:	134
Issue Date:	2014
Publisher / Ed. Institution:	De Gruyter
ISSN:	1609-4840 1609-9389
Language:	English
Subjects:	Modeling error; Dimension reduction; Thin domain; A posteriori error estimate
Subject (DDC):	510: Mathematics
Abstract:	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.
Further description:	Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
URI:	https://digitalcollection.zhaw.ch/handle/11475/29622
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

Files in This Item:

File	Description	Size	Format
2014_Samrowski_Combined-error-estimates-dimension-reduction.pdf		394.48 kB	Adobe PDF	View/Open

Show full item record

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.