A Localized Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910061016645632 |
|---|---|
| author | Hauck, Moritz Målqvist, Axel Mosquera, Malin |
| author_facet | Hauck, Moritz Målqvist, Axel Mosquera, Malin |
| contents | We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition (LOD) framework and constructs locally supported, problem-adapted basis functions on a coarse mesh that does not need to resolve the coefficient oscillations. These basis functions are obtained in parallel by solving localized fine-scale problems. Our a priori error analysis shows that the method achieves optimal convergence with respect to the coarse mesh size, independent of the coefficient regularity, with an exponentially decaying localization error. Numerical experiments validate these theoretical findings and demonstrate the computational viability of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Localized Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems Hauck, Moritz Målqvist, Axel Mosquera, Malin Numerical Analysis 65N12, 65N15, 65N30 We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition (LOD) framework and constructs locally supported, problem-adapted basis functions on a coarse mesh that does not need to resolve the coefficient oscillations. These basis functions are obtained in parallel by solving localized fine-scale problems. Our a priori error analysis shows that the method achieves optimal convergence with respect to the coarse mesh size, independent of the coefficient regularity, with an exponentially decaying localization error. Numerical experiments validate these theoretical findings and demonstrate the computational viability of the method. |
| title | A Localized Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems |
| topic | Numerical Analysis 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2510.09442 |