A numerical existence proof of nodal lines for the first eigenfunction of the plate equation

DOI10.1007/BF01781561zbMath0854.65092OpenAlexW2022877721MaRDI QIDQ1924928

Christian Wieners

Publication date: 27 January 1997

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01781561

zbMATH Keywords

finite elementerror boundseigenfunctionsinterval arithmeticplateeigenvalue inclusionselliptic eigenvalue problems of fourth order

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 (15)

Asymptotic first eigenvalue estimates for the biharmonic operator on a rectangle ⋮ Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems ⋮ Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem ⋮ Spectral analysis of a generalized buckling problem on a ball ⋮ Nodal properties of eigenfunctions of a generalized buckling problem on balls ⋮ Acceleration of stabilized finite element discretizations for the Stokes eigenvalue problem ⋮ Generalized tight \(p\)-frames and spectral bounds for Laplace-like operators ⋮ Asymptotic expansions and extrapolations of eigenvalues for the Stokes problem by mixed finite element methods ⋮ An efficient direct solver for a class of mixed finite element problems ⋮ Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems ⋮ A multilevel correction method for Stokes eigenvalue problems and its applications ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Minimization of inhomogeneous biharmonic eigenvalue problems ⋮ A meshfree method based on radial basis functions for the eigenvalues of transient Stokes equations ⋮ The triangular spectral element method for Stokes eigenvalues

Cites Work

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• Numerical solution of partial differential equations. Transl. from the German by Peter R. Wadsack
• On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle
• Results of the eigenvalue problem for the plate equation
• Bounds for eigenvalues of second-order elliptic differential operators
• Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
• On the fundamental eigenfunctions of a clamped punctured disk
• Iterative solution of the stream function-vorticity formulation of the Stokes problem, applications to the numerical simulation of incompressible viscous flow
• Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems
• On the Construction of Series Solutions to the First Biharmonic Boundary Value Problem on a Rectangle
• On the Structure of Solutions $\Delta ^2 u = \lambda u$ Which Satisfy the Clamped Plate Conditions on a Right Angle
• Block Five Diagonal Matrices and the Fast Numerical Solution of the Biharmonic Equation

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