A new exact, closed-form a priori global error estimator for second- and higher-order time-integration methods for linear elastodynamics

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Abstract

In our recent papers, we suggested a new two-stage time-integration procedure for linear elastodynamics problems and showed that for long-term integration, time-integration methods with zero numerical dissipation are very effective for all linear elastodynamics problems, including structural dynamics, wave propagation and impact problems. In this paper, we have derived a new exact, closed-form a priori global error estimator for time integration of linear elastodynamics by the trapezoidal rule and the high-order time continuous Galerkin (TCG) methods with zero numerical dissipation (these methods correspond to the diagonal of the Padé approximation table). The new a priori global error estimator allows the selection of the size (the number) of time increments for the indicated time-integration methods at the prescribed accuracy as well as the comparison of the effectiveness of the second- and high-order TCG methods at different observation times. A numerical example shows a good agreement between theoretical and numerical results.

Original languageEnglish
Pages (from-to)1066-1084
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Volume88
Issue number10
DOIs
StatePublished - Dec 9 2011

Keywords

  • A priori error estimator
  • Elastodynamics
  • Global error in time
  • Time integration

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