High-Precision Eigenvalue Bound for the Laplacian with Singularities

DOI10.1007/978-3-662-43799-5_23zbMath1336.65186OpenAlexW131570602MaRDI QIDQ2799568

Shin'ichi Oishi, Tomoaki Okayama, Xuefeng Liu

Publication date: 12 April 2016

Published in: Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-43799-5_23

zbMATH Keywords

algorithmnumerical examplefinite element methodeigenvalue probleminterval arithmeticLaplacianeigenfunctionelliptic operatorrounding errorverified computationLehmann-Goerisch's theorem

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) Roundoff error (65G50) General methods in interval analysis (65G40) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (3)

Fully computable a posteriori error bounds for eigenfunctions ⋮ Projection-based guaranteed \(L^2\) error bounds for finite element approximations of Laplace eigenfunctions ⋮ Sharp numerical inclusion of the best constant for embedding \(H_0^1(\Omega) \hookrightarrow L^p(\Omega)\) on bounded convex domain

Uses Software

• Mathematica
• INTLAB

Cites Work

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• The calculation of guaranteed bounds for eigenvalues using complementary variational principles
• New solutions of the Gelfand problem
• Optimale Eigenwerteinschließungen
• Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
• Mixed and Hybrid Finite Element Methods
• Approximation theory methods for solving elliptic eigenvalue problems
• Chebyshev Polynomial Approximations for the L-Membrane Eigenvalue Problem

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