A priori error estimates for explicit finite element for linear elasto-dynamics by Galerkin method and central difference method.

DOI10.1016/j.cma.2003.08.002zbMath1054.74062OpenAlexW1975711468MaRDI QIDQ1421025

Shen-rong Wu

Publication date: 23 January 2004

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.2003.08.002

zbMATH Keywords

Galerkin methoda priori error estimateExplicit finite elementTransient dynamicsOptimal convergence rateCentral difference method

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite difference methods applied to problems in solid mechanics (74S20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (11)

Solution verification for explicit transient dynamics problems in the presence of hourglass and contact forces ⋮ Lumped mass matrix in explicit finite element method for transient dynamics of elasticity ⋮ Bi-penalty stabilized technique with predictor-corrector time scheme for contact-impact problems of elastic bars ⋮ On the enriched mixed Galerkin method with \(\theta\) scheme for the elastic wave equation ⋮ Numerical treatment for some abstract degenerate second-order evolutionary problem ⋮ A variational principle for dynamic contact with large deformation ⋮ Dynamical analysis of Kirchhoff plates by an explicit time integration Morley element method ⋮ A priori error estimation of a four-node Reissner--Mindlin plate element for elasto-dynamics ⋮ Vibration analysis of plane elasticity problems by the \(C^0\)-continuous time stepping finite element method ⋮ Galerkin Finite Element Approximation of General Linear Second Order Hyperbolic Equations ⋮ Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension

Cites Work

• A priori estimates for mixed finite element methods for the wave equation
• Galerkin methods for parabolic equations with nonlinear boundary conditions
• Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
• Convergence, accuracy and stability of finite element approximations of a class of non‐linear hyperbolic equations
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