Abstract

This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$, $\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization.

Keywords

  1. numerical homogenization
  2. stochastic homogenization
  3. quantitative theory
  4. a priori error estimates
  5. uncertainty
  6. model reduction

MSC codes

  1. 35R60
  2. 65N12
  3. 65N15
  4. 65N30
  5. 73B27
  6. 74Q05

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 660 - 674
ISSN (online): 1095-7170

History

Submitted: 27 December 2019
Accepted: 30 November 2020
Published online: 9 March 2021

Keywords

  1. numerical homogenization
  2. stochastic homogenization
  3. quantitative theory
  4. a priori error estimates
  5. uncertainty
  6. model reduction

MSC codes

  1. 35R60
  2. 65N12
  3. 65N15
  4. 65N30
  5. 73B27
  6. 74Q05

Authors

Affiliations

Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : 865751

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