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 convergenceof the
approximate problems is close to optimal.
