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arXiv · 1808.08148

Guaranteed eigenvalue bounds for the Steklov eigenvalue problem

Chun'guang You·Hehu Xie·Xuefeng Liu
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Abstract

To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigenvalue problems. In practical eigenvalue estimation, the Crouzeix--Raviart finite element method (FEM) along with quantitative error estimation is adopted. Numerical experiments for eigenvalue problems defined on a square domain and an L-shaped domain are provided to validate the precision of computed eigenvalue bounds.

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Chun'guang You, Hehu Xie, Xuefeng Liu. 2018-08-24. Guaranteed eigenvalue bounds for the Steklov eigenvalue problem. https://arxiv.org/abs/1808.08148

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