Numerical approximation of the first $p$-Laplace eigenpair
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_ | 1866911516929818624 |
|---|---|
| author | Potgieter, Hannah Fetecau, Razvan C. Ruuth, Steven J. |
| author_facet | Potgieter, Hannah Fetecau, Razvan C. Ruuth, Steven J. |
| contents | We approximate the first Dirichlet eigenpair of the $p$-Laplace operator for $2 \leq p < \infty$ on both Euclidean and surface domains. We emphasize large $p$ values and discuss how the $p \to \infty$ limit connects to the underlying geometry of our domain. Working with large $p$ values introduces significant numerical challenges. We present a surface finite element numerical scheme that combines a Newton inverse-power iteration with a new domain rescaling strategy, which enables stable computations for large $p$. Numerical experiments in $1$D, planar domains, and surfaces embedded in $\mathbb{R}^3$ demonstrate the accuracy and robustness of our approach and show convergence towards the $p \to \infty$ limiting behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical approximation of the first $p$-Laplace eigenpair Potgieter, Hannah Fetecau, Razvan C. Ruuth, Steven J. Numerical Analysis Spectral Theory We approximate the first Dirichlet eigenpair of the $p$-Laplace operator for $2 \leq p < \infty$ on both Euclidean and surface domains. We emphasize large $p$ values and discuss how the $p \to \infty$ limit connects to the underlying geometry of our domain. Working with large $p$ values introduces significant numerical challenges. We present a surface finite element numerical scheme that combines a Newton inverse-power iteration with a new domain rescaling strategy, which enables stable computations for large $p$. Numerical experiments in $1$D, planar domains, and surfaces embedded in $\mathbb{R}^3$ demonstrate the accuracy and robustness of our approach and show convergence towards the $p \to \infty$ limiting behavior. |
| title | Numerical approximation of the first $p$-Laplace eigenpair |
| topic | Numerical Analysis Spectral Theory |
| url | https://arxiv.org/abs/2512.10122 |