Adaptive Crouzeix-Raviart finite elements for the first eigenpair of $p$-Laplacian
Abstract
In this paper, we propose and analyze an adaptive Crouzeix-Raviart finite element method for computing the first Dirichlet eigenpair of the -Laplacian problem. We prove that the sequence of error estimators produced by the adaptive algorithm has a vanishing limit and that, starting from a fine initial mesh, the relevant sequence of approximate eigenvalues converges to the first eigenvalue and the distance in a mesh-dependent broken norm between discrete eigenfunctions and the set composed of relevant continuous eigenfunctions also tends to zero. The analysis hinges on establishing a compactness property for Crouzeix-Raviart finite elements over a sequence of adaptively generated meshes, which represents key theoretical challenges and novelties. We present numerical results to illustrate the advantage of the proposed algorithm.
Cite
@article{arxiv.2508.02077,
title = {Adaptive Crouzeix-Raviart finite elements for the first eigenpair of $p$-Laplacian},
author = {Guanglian Li and Yueqi Wang and Yifeng Xu},
journal= {arXiv preprint arXiv:2508.02077},
year = {2025}
}