Volume 56, Number 4, July-August 2022
|Page(s)||1451 - 1481|
|Published online||13 July 2022|
Numerical homogenization of fractal interface problems
Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
2 Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
* Corresponding author: firstname.lastname@example.org
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.