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A time dependent approach for removing the cell boundary error in elliptic homogenization problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-6321-8619
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, 206-227 p.Article in journal (Refereed) PublishedText
Abstract [en]

This paper concerns the cell-boundary error present in multiscale algorithms for elliptic homogenization problems. Typical multiscale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. To solve the micro model, boundary conditions are required on the boundary of the microscopic domain. Imposing a naive boundary condition leads to O(epsilon/eta) error in the computation, where epsilon is the size of the microscopic variations in the media and eta is the size of the micro-domain. The removal of this error in modern multiscale algorithms still remains an important open problem. In this paper, we present a time-dependent approach which is general in terms of dimension. We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of epsilon/eta in the periodic setting. Additionally, we present numerical evidence showing that the method improves the O(epsilon/eta) error to O(epsilon) in general non-periodic media.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 314, 206-227 p.
Keyword [en]
Multiscale problems, Homogenization, Elliptic PDEs
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-186597DOI: 10.1016/ 000374122100013OAI: diva2:932256

QC 20160601

Available from: 2016-06-01 Created: 2016-05-13 Last updated: 2016-06-01Bibliographically approved

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Runborg, Olof
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