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Pointwise a Posteriori Error Estimators for Multiple and Clustered Eigenvalue Computations
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DOI：10.1007/s10915-026-03378-6.png)
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Abstract
En 中文
In this work, we propose a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a posteriori error estimator is reliable and efficient, up to some logarithmic factors of the mesh size. The constants involved in the reliability and efficiency are independent of the gaps among the targeted eigenvalues, the mesh size and the number of mesh level. Specially, we obtain a by-product that edge residuals dominate the a posteriori error in the sense of $$L^{\infty }$$ -norm when the linear element is used. With the aid of the weighted Sobolev stability of the $$L^2$$ -projection, we also propose a new method to prove the reliability of the a posteriori error estimator for higher order finite elements. A key ingredient in the a posteriori error analysis is some new estimates for regularized derivative Green’s functions. Some numerical experiments verify our theoretical results.
Keywords:
Elliptic eigenvalue problems
Multiple and clustered eigenvalues
Maximum norm
Finite element methods
A posteriori error estimator
Journal
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3.3
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652
Citations:
9.6K
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