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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
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