Repository: Freie Universit├Ąt Berlin, Math Department

Fractal homogenization of multiscale interface problems

Heida, M. and Kornhuber, R. and Podlesny, J. (2017) Fractal homogenization of multiscale interface problems. SFB 1114 Preprint in arXiv . pp. 1-17. (Submitted)

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Official URL: https://arxiv.org/abs/1712.01172

Abstract

Inspired from geological problems, we introduce a new geometrical setting for homogenization of a well known and well studied problem of an elliptic second order differential operator with jump conditions on a multiscale network of interfaces. The geometrical setting is fractal and hence neither periodic nor stochastic methods can be applied to the study of such kind of multiscale interface problem. Instead, we use the fractal nature of the geometric structure to introduce smoothed problems and apply methods from a posteriori theory to derive an estimate for the order of convergence. Computational experiments utilizing an iterative homogenization approach illustrate that the theoretically derived order of convergence of the approximate problems is close to optimal.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2144
Deposited By: Ekaterina Engel
Deposited On:05 Dec 2017 14:07
Last Modified:05 Dec 2017 14:53

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