Guaranteed Eigenvalue Bounds for the Steklov Eigenvalue Problem

DOI10.1137/18M1189592zbMath1427.65384arXiv1808.08148OpenAlexW2963566796MaRDI QIDQ5232291

Hehu Xie, Xuefeng Liu, Chun'guang You

Publication date: 2 September 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08148

zbMATH Keywords

eigenvalue boundsSteklov eigenvalue problemCrouzeix-Raviart finite element method

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Acceleration of convergence in numerical analysis (65B99)

Related Items (14)

Mixed methods and lower eigenvalue bounds ⋮ Fully computable a posteriori error bounds for eigenfunctions ⋮ Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients. ⋮ Error-constant estimation under the maximum norm for linear Lagrange interpolation ⋮ Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysis ⋮ Projection-based guaranteed \(L^2\) error bounds for finite element approximations of Laplace eigenfunctions ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ A DRBEM approximation of the Steklov eigenvalue problem ⋮ Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues ⋮ A counterexample to Payne's nodal line conjecture with few holes ⋮ Guaranteed lower eigenvalue bounds for two spectral problems arising in fluid mechanics ⋮ Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms ⋮ Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains ⋮ Isoparametric numerical integration on enriched 4D simplicial elements

Uses Software

• INTLAB

Cites Work

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