Fractal homogenization of a multiscale interface problem
- Heida, Martin
- Kornhuber, Ralf
- Podlesny, Joscha
2010 Mathematics Subject Classification
- 74B05 74Qxx 74Q05 65M22 65M55
- Multiscale interfaces, fractal homogenization, elasticity, jump conditions, multiscale numerics
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 condition 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.
- Multiscale Model. Simul., 18 (2020), pp. 294--314, DOI 10.1137/18M1204759 .