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.
Keywords: Fractal interface problems, multiscale finite elements, subspace decomposition, Clément-type projection
@article{M2AN_2022__56_4_1451_0,
author = {Kornhuber, Ralf and Podlesny, Joscha and Yserentant, Harry},
title = {Numerical homogenization of fractal interface problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1451--1481},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/m2an/2022046},
mrnumber = {4451302},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022046/}
}
TY - JOUR AU - Kornhuber, Ralf AU - Podlesny, Joscha AU - Yserentant, Harry TI - Numerical homogenization of fractal interface problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1451 EP - 1481 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022046/ DO - 10.1051/m2an/2022046 LA - en ID - M2AN_2022__56_4_1451_0 ER -
%0 Journal Article %A Kornhuber, Ralf %A Podlesny, Joscha %A Yserentant, Harry %T Numerical homogenization of fractal interface problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1451-1481 %V 56 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022046/ %R 10.1051/m2an/2022046 %G en %F M2AN_2022__56_4_1451_0
Kornhuber, Ralf; Podlesny, Joscha; Yserentant, Harry. Numerical homogenization of fractal interface problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 4, pp. 1451-1481. doi: 10.1051/m2an/2022046
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