Computation of local and quasi-local effective diffusion tensors in elliptic homogenization
Computation of local and quasi-local effective diffusion tensors in elliptic homogenization
Dokument öffnen (2MB)Datum der Veröffentlichung
08.2016Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11855
Inhalt
This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the involved integral kernel motivates the use of a diagonal approximation and, hence, a localized piecewise constant coefficient. This local model turns out to be appropriate when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. An a priori error analysis of the local model is presented and illustrated in numerical experiments.
Schlagwörter
numerical homogenization, multiscale method, upscaling, a priori error estimates, a posteriori error estimates
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1137/16M1088533Reihe, Nummer
INS Preprints ; 1619Gallistl, Dietmar; Peterseim, Daniel: Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. In: INS Preprints, 1619.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11855
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11855
@unpublished{handle:20.500.11811/11855,
author = {{Dietmar Gallistl} and {Daniel Peterseim}},
title = {Computation of local and quasi-local effective diffusion tensors in elliptic homogenization},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = aug,
INS Preprints},
volume = 1619,
note = {This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the involved integral kernel motivates the use of a diagonal approximation and, hence, a localized piecewise constant coefficient. This local model turns out to be appropriate when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. An a priori error analysis of the local model is presented and illustrated in numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11855}
}
author = {{Dietmar Gallistl} and {Daniel Peterseim}},
title = {Computation of local and quasi-local effective diffusion tensors in elliptic homogenization},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = aug,
INS Preprints},
volume = 1619,
note = {This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the involved integral kernel motivates the use of a diagonal approximation and, hence, a localized piecewise constant coefficient. This local model turns out to be appropriate when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. An a priori error analysis of the local model is presented and illustrated in numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11855}
}
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