Stability analysis of linear multistep methods for classical elastodynamics

DOI10.1016/j.cma.2004.01.012zbMath1067.74597OpenAlexW2061736158MaRDI QIDQ704434

Ignacio Romero

Publication date: 13 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.cma.2004.01.012

zbMATH Keywords

Modal analysisFinite elementsGlobal energy stability

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in solid mechanics (74S20)

Related Items (2)

Unscented Kalman filtering for nonlinear structural dynamics ⋮ Analysis of error estimators for the semidiscrete equations of linear solid and structural dynamics

Cites Work

• On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods
• On the stability and convergence of fully discrete solutions in linear elastodynamics
• Evaluation of numerical integration methods in elastodynamics
• A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
• Multistep-Galerkin Methods for Hyperbolic Equations
• On the Convergence of Galerkin Approximation Schemes for Second-Order Hyperbolic Equations in Energy and Negative Norms
• Linear Multistep Methods and Galerkin Procedures for Initial Boundary Value Problems
• Semidiscrete and single step fully discrete approximations for second order hyperbolic equations
• On the variational method in the direct integration of the transient structural response
• Discussion of a paper By K. K. GUPTA
• The automatic integration of ordinary differential equations
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