Reversed stability conditions in transient finite element analysis
type: Item
instance of: scholarly article
title: Reversed stability conditions in transient finite element analysis
zbMATH Open document ID: 0647.73035
DOI: 10.1016/0045-7825(88)90109-0
author: David S. Malkus
author: Michael E. Plesha
author: Meng-Ru Liu
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: Numerical methods which introduce artificially unstable modes are discussed. In structural and elastodynamics these result from optimal mass lumping with higher-order elements. In fluid mechanics an additional source of these modes can be a penalty function with alternating signs. These modes yield unstable modal equations; however, they do not necessarily imply unstable transient integration in the presence of algorithmic damping. Stable integration can be achieved by satisfying a stability condition in which the roles of space-step and time-step are reversed. Elatodyamics, the Navier-Stokes equations, and non-Newtonian fluids provide numerical examples.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 4057140
zbMATH Keywords: numerical experiment
zbMATH Keywords: unstable high-frequency modes
zbMATH Keywords: semidiscrete equations
zbMATH Keywords: algorithmic damping
zbMATH Keywords: Newmark method
zbMATH Keywords: generalized trapezoidal methods
zbMATH Keywords: artificially unstable modes
zbMATH Keywords: elastodynamics
zbMATH Keywords: optimal mass lumping
zbMATH Keywords: higher-order elements
zbMATH Keywords: fluid mechanics
zbMATH Keywords: penalty function with alternating signs
zbMATH Keywords: unstable modal equations
zbMATH Keywords: Stable integration
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90109-0
OpenAlex ID: W2010165270
cites work: Zero and negative masses in finite element vibration and transient analysis
cites work: Stability of explicit‐implicit mesh partitions in time integration
cites work: Q3671072
cites work: Q3773481
cites work: Analysis of the Finite Element Variable Penalty Method for Stokes Equations
cites work: A finite element for incompressible plane flows of fluids with memory
cites work: Obtaining error estimates for optimally constrained incompressible finite elements
cites work: Finite element analysis of incompressible viscous flows by the penalty function formulation
cites work: FIDAP (A Fluid Dynamics Analysis Program)
cites work: Q3926196
cites work: Divisor structure of finite element eigenproblems arising from negative and zero masses
cites work: Q5674306
cites work: Eigenproblems associated with the discrete LBB condition for incompressible finite elements
description: scientific article; zbMATH DE number 4057140