An element eigenvalue theorem and its application for stable time steps

DOI10.1016/0045-7825(89)90069-8zbMath0688.73047OpenAlexW2085077600MaRDI QIDQ1264035

Jerry I. Lin

Publication date: 1989

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(89)90069-8

zbMATH Keywords

accurate estimates on frequenciesbounds on the extremal element eigenvalues for numerically integrated elementsselective-reduced integrated 4-node quadrilateral elementstwo or more quadrature points

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (5)

On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration ⋮ The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics ⋮ Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations ⋮ What are \(C\) and \(h\)?: Inequalities for the analysis and design of finite element methods ⋮ Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems

Cites Work

• Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral
• Eigenvalues and stable time steps for the bilinear Mindlin plate element
• Discretization and computational errors in high-order finite elements
• Optimal gradient minimization scheme for finite element eigenproblems
• Condition of finite element matrices generated from nonuniform meshes.
• Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number
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