Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas

DOI10.1016/0377-0427(92)90016-QzbMath0762.65056OpenAlexW2005361151MaRDI QIDQ1195738

S. Singh

Publication date: 18 January 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(92)90016-q

zbMATH Keywords

numerical resultsdiscrete spectrumorder of convergenceeigenpairsoptimal error estimateLagrange finite elementsLobatto quadrature formulalumped mass discrete eigenvalue problemsecond order elliptic eigenvalue problems

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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 (13)

Spectral element computation of high-frequency leaky modes in three-dimensional solid waveguides ⋮ Finite element approximation for 2nd order elliptic eigenvalue problems with nonlocal boundary or transition conditions ⋮ Lumped mass matrix in explicit finite element method for transient dynamics of elasticity ⋮ A variational approximation method for 2nd order elliptic eigenvalue problems in a composite structure with nonstandard boundary conditions ⋮ An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures ⋮ On a finite element method for second order elliptic eigenvalue problems with nonlocal direchlet boundary conditions ⋮ On a variational approximation method for a class of elliptic eigenvalue problems in composite structures ⋮ Analysis and spectral element solution of nonlinear integral equations of Hammerstein type ⋮ Spectral element approximation of Fredholm integral eigenvalue problems ⋮ Nonlinear transient dynamic analysis by explicit finite element with iterative consistent mass matrix ⋮ High-order Mass-lumped Schemes for Nonlinear Degenerate Elliptic Equations ⋮ Unnamed Item ⋮ A finite element method for differential eigenvalue problems with mixed classical and (semi-)periodic boundary conditions

Cites Work

• Estimation of the effect of numerical integration in finite element eigenvalue approximation
• Convergence of the finite element method applied to the eigenvalue problem \(\Delta u+\lambda u=0\)
• Bounds for a class of linear functionals with applications to Hermite interpolation
• Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to Eigenfunctions
• Equivalent Norms for Sobolev Spaces
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