Asymptotic meshes from $r$-variational adaptation methods for static problems in one dimension
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909878390358016 |
|---|---|
| author | Hun, Darith Moës, Nicolas Olbermann, Heiner |
| author_facet | Hun, Darith Moës, Nicolas Olbermann, Heiner |
| contents | We consider the minimization of integral functionals in one dimension and their approximation by $r$-adaptive finite elements. Including the grid of the FEM approximation as a variable in the minimization, we are able to show that the optimal grid configurations have a well-defined limit when the number of nodes in the grid is being sent to infinity. This is done by showing that the suitably renormalized energy functionals possess a limit in the sense of $Γ$-convergence. We provide numerical examples showing the closeness of the optimal asymptotic mesh obtained as a minimizer of the $Γ$-limit to the optimal finite meshes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic meshes from $r$-variational adaptation methods for static problems in one dimension Hun, Darith Moës, Nicolas Olbermann, Heiner Numerical Analysis Analysis of PDEs 49J45, 49Q10, 65N30, 65N50, 74S05 We consider the minimization of integral functionals in one dimension and their approximation by $r$-adaptive finite elements. Including the grid of the FEM approximation as a variable in the minimization, we are able to show that the optimal grid configurations have a well-defined limit when the number of nodes in the grid is being sent to infinity. This is done by showing that the suitably renormalized energy functionals possess a limit in the sense of $Γ$-convergence. We provide numerical examples showing the closeness of the optimal asymptotic mesh obtained as a minimizer of the $Γ$-limit to the optimal finite meshes. |
| title | Asymptotic meshes from $r$-variational adaptation methods for static problems in one dimension |
| topic | Numerical Analysis Analysis of PDEs 49J45, 49Q10, 65N30, 65N50, 74S05 |
| url | https://arxiv.org/abs/2510.26375 |