Robust numerical upscaling of elliptic multiscale problems at high contrast
Robust numerical upscaling of elliptic multiscale problems at high contrast
View/Date of Publication
01.2016Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11860
Abstract
We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of H1 into the image and the kernel of some novel stable quasi-interpolation operators with local L2–approximation properties, independent of the contrast. We identify a set of sufficient assumptions on these quasi-interpolation operators that guarantee in principle optimal convergence without pre-asymptotic effects for high-contrast coefficients. We then give an example of a suitable operator and establish the assumptions for a particular class of high-contrast coefficients. So far this is not possible without any pre-asymptotic effects, but the optimal convergence is independent of the contrast and the asymptotic range is largely improved over other discretisation schemes. The new framework is sufficiently flexible to allow also for other choices of quasi-interpolation operators and the potential for fully robust numerical upscaling at high contrast.
Subjects
Finite Element, Multiscale, Upscaling, Computational Homogenization, High Contrast
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1515/cmam-2016-0022Part of Series
INS Preprints ; 1603Peterseim, Daniel; Scheichl, Robert: Robust numerical upscaling of elliptic multiscale problems at high contrast. In: INS Preprints, 1603.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11860
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11860
@unpublished{handle:20.500.11811/11860,
author = {{Daniel Peterseim} and {Robert Scheichl}},
title = {Robust numerical upscaling of elliptic multiscale problems at high contrast},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = jan,
INS Preprints},
volume = 1603,
note = {We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of H1 into the image and the kernel of some novel stable quasi-interpolation operators with local L2–approximation properties, independent of the contrast. We identify a set of sufficient assumptions on these quasi-interpolation operators that guarantee in principle optimal convergence without pre-asymptotic effects for high-contrast coefficients. We then give an example of a suitable operator and establish the assumptions for a particular class of high-contrast coefficients. So far this is not possible without any pre-asymptotic effects, but the optimal convergence is independent of the contrast and the asymptotic range is largely improved over other discretisation schemes. The new framework is sufficiently flexible to allow also for other choices of quasi-interpolation operators and the potential for fully robust numerical upscaling at high contrast.},
url = {https://hdl.handle.net/20.500.11811/11860}
}
author = {{Daniel Peterseim} and {Robert Scheichl}},
title = {Robust numerical upscaling of elliptic multiscale problems at high contrast},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = jan,
INS Preprints},
volume = 1603,
note = {We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of H1 into the image and the kernel of some novel stable quasi-interpolation operators with local L2–approximation properties, independent of the contrast. We identify a set of sufficient assumptions on these quasi-interpolation operators that guarantee in principle optimal convergence without pre-asymptotic effects for high-contrast coefficients. We then give an example of a suitable operator and establish the assumptions for a particular class of high-contrast coefficients. So far this is not possible without any pre-asymptotic effects, but the optimal convergence is independent of the contrast and the asymptotic range is largely improved over other discretisation schemes. The new framework is sufficiently flexible to allow also for other choices of quasi-interpolation operators and the potential for fully robust numerical upscaling at high contrast.},
url = {https://hdl.handle.net/20.500.11811/11860}
}
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