2025/11/10 by Li, Zhenglei, Liang, Qigang, Xu, Xuejun · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2511.06815
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∞-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.