Numerical stochastic homogenization by quasi-local effective diffusion tensors
Numerical stochastic homogenization by quasi-local effective diffusion tensors
View/Date of Publication
02.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11840
Abstract
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral operator, which can be further compressed to an effective partial differential operator. Error estimates consisting of a priori and a posteriori terms are provided that allow one to quantify the impact of uncertainty in the diffusion coefficient on the expected effective response of the process.
Subjects
numerical homogenization, multiscale method, upscaling, a priori error estimates, a posteriori error estimates, uncertainty, modeling error estimate, model reduction
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.4310/CMS.2019.v17.n3.a3Part of Series
INS Preprints ; 1701Gallistl, Dietmar; Peterseim, Daniel: Numerical stochastic homogenization by quasi-local effective diffusion tensors. In: INS Preprints, 1701.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11840
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11840
@unpublished{handle:20.500.11811/11840,
author = {{Dietmar Gallistl} and {Daniel Peterseim}},
title = {Numerical stochastic homogenization by quasi-local effective diffusion tensors},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = feb,
INS Preprints},
volume = 1701,
note = {This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral operator, which can be further compressed to an effective partial differential operator. Error estimates consisting of a priori and a posteriori terms are provided that allow one to quantify the impact of uncertainty in the diffusion coefficient on the expected effective response of the process.},
url = {https://hdl.handle.net/20.500.11811/11840}
}
author = {{Dietmar Gallistl} and {Daniel Peterseim}},
title = {Numerical stochastic homogenization by quasi-local effective diffusion tensors},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = feb,
INS Preprints},
volume = 1701,
note = {This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral operator, which can be further compressed to an effective partial differential operator. Error estimates consisting of a priori and a posteriori terms are provided that allow one to quantify the impact of uncertainty in the diffusion coefficient on the expected effective response of the process.},
url = {https://hdl.handle.net/20.500.11811/11840}
}
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