Constructing both lower and upper bounds for the eigenvalues of elliptic operators by nonconforming finite element methods

DOI10.1007/s00211-014-0688-zzbMath1326.65156OpenAlexW2170446622MaRDI QIDQ495540

Quan Shen, Yunqing Huang, Jun Hu

Publication date: 14 September 2015

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-014-0688-z

zbMATH Keywords

convergencenumerical exampleselliptic operatorseigenfunctionupper bounds of eigenvaluesnonconforming finite element methods

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) 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)

Related Items (11)

Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations ⋮ Guaranteed lower bounds for eigenvalues of elliptic operators ⋮ Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues ⋮ A multi-level mixed element method for the eigenvalue problem of biharmonic equation ⋮ The lower/upper bound property of approximate eigenvalues by nonconforming finite element methods for elliptic operators ⋮ The Weak Galerkin Method for Elliptic Eigenvalue Problems ⋮ Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes ⋮ Guaranteed lower eigenvalue bounds for two spectral problems arising in fluid mechanics ⋮ Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation ⋮ Asymptotically Exact A Posteriori Error Estimates of Eigenvalues by the Crouzeix--Raviart Element and Enriched Crouzeix--Raviart Element ⋮ Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains

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