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Guaranteed eigenvalue bounds for the Steklov eigenvalue problem
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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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Lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients
A corrected Crouzeix-Raviart finite element eigenvalue converges from below to the exact Steklov eigenvalue with variable coefficients, at the same order as the uncorrected approximation.
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