### Abstract

This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M\aalqvist and Peterseim [Math. Comp., 83 (2014), pp. 2583--2603], which is based on orthogonal subspace decomposition, is reinterpreted 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. In a periodic setting, the computed localized coefficient is proved to coincide with the classical homogenization limit. An a priori error analysis shows that the local numerical model is appropriate beyond the periodic setting when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. The results are illustrated in numerical experiments.

Original language | English |
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Pages (from-to) | 1530-1552 |

Number of pages | 23 |

Journal | Multiscale Modeling and Simulation |

Volume | 15 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |

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## Cite this

Gallistl, D., & Peterseim, D. (2017). Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization.

*Multiscale Modeling and Simulation*,*15*(4), 1530-1552. https://doi.org/10.1137/16M1088533