Stability of semidiscrete formulations for elastodynamics at small time steps

Eran Grosu, Isaac Harari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Solutions of direct time-integration schemes for elastodynamics that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious oscillations that violate the principle of causality, for example by arising before wave fronts. This degradation is not an artifact of the time-marching scheme, but rather a property of the solution of the semidiscrete formulation itself. An analogy to singularly perturbed elliptic problems provides an upper bound on the time step for the onset of these oscillations. A simple procedure of spatial stabilization is proposed to remove this pathology from implicit time-integration schemes, without affecting unconditional temporal stability. Spatially stabilized implicit time-integration methods are free of noncausal oscillations at small time steps.

Original languageEnglish
Pages (from-to)533-542
Number of pages10
JournalFinite Elements in Analysis and Design
Issue number6-7
StatePublished - Apr 2007


  • Principle of causality
  • Rothe method
  • Semidiscrete
  • Small time step oscillation
  • Spatial stabilization


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