Adaptive Finite Element Approximations of the First Eigenpair Associated with \({p}\)-Laplacian
In this paper, we propose an adaptive finite element method for computing the first eigenpair of the p-Laplacian problem. We prove that by starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous problem, and the distance between discrete eigenfunctions and the normalized eigenfunction set corresponding to the first eigenvalue in W<sup>1,p</sup>-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.
Authors
- Shengfeng Zhu (ORCID: https://orcid.org/0000-0002-4626-9983)
- Yifeng Xu (ORCID: https://orcid.org/0009-0006-3216-1310)
- Guanglian Li (ORCID: https://orcid.org/0000-0003-0615-2681)
- Jessica J. Merten
- Jing Li (ORCID: https://orcid.org/0009-0000-6253-6423)
Institutions
- Shanghai Normal University (CN)
- Numerical Method (China) (CN)
- East China Normal University (CN)
- University of Hong Kong (HK)
Publication Details
- Journal
- SIAM Journal on Scientific Computing
- Published
- 2025-02-06
- DOI
- https://doi.org/10.1137/24m1637052
- Citations
- 3
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 3.01
Funders
- National Natural Science Foundation of China
- Research Grants Council, University Grants Committee
- Science and Technology Commission of Shanghai Municipality
- General Research Fund of Shanghai Normal University