Adaptive FEM with optimal convergence rate for non-self-adjoint eigenvalue problems

Shixi Wang; Hai Bi; Yidu Yang

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arXiv · 2603.12973

Adaptive FEM with optimal convergence rate for non-self-adjoint eigenvalue problems

Shixi Wang·Hai Bi·Yidu Yang

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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.

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Shixi Wang, Hai Bi, Yidu Yang. 2026-03-13. Adaptive FEM with optimal convergence rate for non-self-adjoint eigenvalue problems. https://arxiv.org/abs/2603.12973

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