Results of the eigenvalue problem for the plate equation

DOI10.1007/BF01594119zbMath0458.73065OpenAlexW1982874325MaRDI QIDQ1151777

Wolfgang Hackbusch, Götz Hofmann

Publication date: 1980

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01594119

zbMATH Keywords

46 eigenvaluesbiharmonic plate equationcomputedeigenfunctions plotted

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (5)

Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems ⋮ A numerical existence proof of nodal lines for the first eigenfunction of the plate equation ⋮ Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators ⋮ On the first eigenvalue of the clamped plate ⋮ An efficient direct solver for a class of mixed finite element problems

Cites Work

• Nonconforming finite element methods for eigenvalue problems in linear plate theory
• Asymptotic upper and lower bounds for results of extrapolation methods
• Convergence of Multi-Grid Iterations Applied to Difference Equations
• On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method
• Block Five Diagonal Matrices and the Fast Numerical Solution of the Biharmonic Equation
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