| Issue |
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
|
|
|---|---|---|
| Page(s) | 1451 - 1481 | |
| DOI | https://doi.org/10.1051/m2an/2022046 | |
| Published online | 13 July 2022 | |
Numerical homogenization of fractal interface problems
1
Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
2
Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
* Corresponding author: kornhuber@math.fu-berlin.de
Received:
12
February
2021
Accepted:
2
May
2022
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.
Mathematics Subject Classification: 65N12 / 65N15 / 65F08 / 65F10
Key words: Fractal interface problems / multiscale finite elements / subspace decomposition / Clément-type projection
© The authors. Published by EDP Sciences, SMAI 2022
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