We consider the numerical homogenization of a class of fractal elliptic
interface problems inspired by related mechanical contact problems from the
geosciences. A particular feature is that the solution space depends on the
actual fractal geometry. Our main results concern the construction of
projection operators with suitable stability and approximation properties. The
existence of such projections then allows for the application of existing
concepts from localized orthogonal decomposition (LOD) and successive subspace
correction to construct first multiscale discretizations and iterative
algebraic solvers with scale-independent convergence behavior for this class of
problems
