The lower/upper bound property of approximate eigenvalues by nonconforming finite element methods for elliptic operators

DOI10.1007/s10915-013-9744-6zbMath1301.65117OpenAlexW2044429552MaRDI QIDQ461239

Quan Shen, Yunqing Huang, Jun Hu

Publication date: 10 October 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9744-6

zbMATH Keywords

eigenvalueupper boundlower boundeigenfunctionnonconforming finite elementnumerical resultCrouzeix-Raviart elementMorley elementStokes eigenvalue problemAdini elementbuckling eigenvalue problem of a plateZienkiewicz-type element

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) 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 (12)

Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework ⋮ A weak Galerkin finite element method can compute both upper and lower eigenvalue bounds ⋮ Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations ⋮ Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters ⋮ A new nonconforming mixed finite element scheme for second order eigenvalue problem ⋮ A penalized Crouzeix-Raviart element method for second order elliptic eigenvalue problems ⋮ Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes ⋮ Nonconforming finite element analysis for Poisson eigenvalue problem ⋮ C 0 Interior Penalty Galerkin Method for Biharmonic Eigenvalue Problems ⋮ Solving Eigenvalue Problems in a Discontinuous Approximation Space by Patch Reconstruction ⋮ The lower/upper bound property of the Crouzeix-Raviart element eigenvalues on adaptive meshes ⋮ The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements

Cites Work

• Eigenvalue approximations from below using Morley elements
• Constructing both lower and upper bounds for the eigenvalues of elliptic operators by nonconforming finite element methods
• A note on the preconditioned Gauss--Seidel (GS) method for linear systems
• A new class of Zienkiewicz-type non-conforming element in any dimensions
• Estimation of interpolation error constants for the \(P_0\) and \(P_1\) triangular finite elements
• Nonconforming finite element methods for eigenvalue problems in linear plate theory
• Asymptotic lower bounds for eigenvalues by nonconforming finite element methods
• A high accuracy post-processing algorithm for the eigenvalues of elliptic operators
• Eigenvalue approximation from below using non-conforming finite elements
• Lower bounds of the discretization error for piecewise polynomials
• Finite element approximation of eigenvalue problems
• Simple nonconforming quadrilateral Stokes element
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
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