Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918288730095616 |
|---|---|
| author | Alber, Christian Holbach, Lukas |
| author_facet | Alber, Christian Holbach, Lukas |
| contents | We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a correction from an optimal spectral coarse space, which is obtained from a generalized eigenproblem. The global solution is then assembled via a partition of unity. We prove nearly exponential decay of the approximation error for second-order elliptic problems with highly heterogeneous diffusion discretized by a weighted symmetric interior-penalty DG scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes Alber, Christian Holbach, Lukas Numerical Analysis 65N15, 65N30, 65N55 We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a correction from an optimal spectral coarse space, which is obtained from a generalized eigenproblem. The global solution is then assembled via a partition of unity. We prove nearly exponential decay of the approximation error for second-order elliptic problems with highly heterogeneous diffusion discretized by a weighted symmetric interior-penalty DG scheme. |
| title | Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes |
| topic | Numerical Analysis 65N15, 65N30, 65N55 |
| url | https://arxiv.org/abs/2510.21289 |