Adaptive FEM with optimal convergence rate for non-self-adjoint eigenvalue problems
Numerical Analysis
2026-03-16 v1 Numerical Analysis
Spectral Theory
Abstract
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered eigenvalues with the help of the error estimators of finite element solutions for the corresponding source problems, and prove the equivalence between these two estimators. We propose an adaptive algorithm for the eigenvalue cluster and demonstrate that it achieves the optimal convergence rate.We also provide numerical experiments to support our theoretical findings.
Cite
@article{arxiv.2603.12973,
title = {Adaptive FEM with optimal convergence rate for non-self-adjoint eigenvalue problems},
author = {Shixi Wang and Hai Bi and Yidu Yang},
journal= {arXiv preprint arXiv:2603.12973},
year = {2026}
}