Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems

DOI10.1007/BF02684402zbMath0883.65082MaRDI QIDQ1365537

Christian Wieners

Publication date: 4 September 1997

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

numerical resultseigenvaluesinterval analysiserror boundsclamped plate probleminclusion intervalsboundary homotopy methodfourth-order elliptic differential equations

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Interval and finite arithmetic (65G30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (11)

A numerical existence proof of nodal lines for the first eigenfunction of the plate equation ⋮ Sinc-Galerkin solution to the clamped plate eigenvalue problem ⋮ On the convergence of a two-level preconditioned Jacobi–Davidson method for eigenvalue problems ⋮ The two-grid discretization of Ciarlet-Raviart mixed method for biharmonic eigenvalue problems ⋮ Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method. ⋮ Asymptotic expansion and extrapolation for the eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet-Raviart scheme ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems ⋮ C 0 Interior Penalty Galerkin Method for Biharmonic Eigenvalue Problems ⋮ A new method using \(C^0\)IPG for the biharmonic eigenvalue problem ⋮ The triangular spectral element method for Stokes eigenvalues

Cites Work

• Numerical solution of partial differential equations. Transl. from the German by Peter R. Wadsack
• Zur Methode der finiten Elemente
• 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
• Iterative solution of the stream function-vorticity formulation of the Stokes problem, applications to the numerical simulation of incompressible viscous flow
• A numerical existence proof of nodal lines for the first eigenfunction of the plate equation
• On some approximate methods concerning the operators \(T^*T\)
• Analysis of Vibration Eigenfrequencies of a Thin Plate by the Keller-Rubinow Wave Method I: Clamped Boundary Conditions with Rectangular or Circular Geometry
• Eigenwertschranken für Eigenwertaufgaben mit partiellen Differentialgleichungen
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