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arXiv · 2511.06815

Pointwise A Posteriori Error Estimators for Elliptic Eigenvalue Problems

Zhenglei Li·Qigang Liang·Xuejun Xu
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Abstract

In this work, we propose and analyze a pointwise a posteriori error estimator for simple eigenvalues of elliptic eigenvalue problems with adaptive finite element methods (AFEMs). We prove the reliability and efficiency of the residual-type a posteriori error estimator in the sense of $L^{\infty}$-norm, up to a logarithmic factor of the mesh size. For theoretical analysis, we also propose a theoretical and non-computable estimator, and then analyze the relationship between computable estimator and theoretical estimator. A key ingredient in the a posteriori error analysis is some new estimates for regularized derivative Green's functions. This methodology is also extended to the nonconforming finite element approximations. Some numerical experiments verify our theoretical results.

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Zhenglei Li, Qigang Liang, Xuejun Xu. 2025-11-10. Pointwise A Posteriori Error Estimators for Elliptic Eigenvalue Problems. https://arxiv.org/abs/2511.06815

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