Numerical Homogenization of Fractal Interface Problems
Numerical Analysis
2020-07-23 v1 Numerical Analysis
Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.2007.11479,
title = {Numerical Homogenization of Fractal Interface Problems},
author = {Ralf Kornhuber and Joscha Podlesny and Harry Yserentant},
journal= {arXiv preprint arXiv:2007.11479},
year = {2020}
}