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

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. Copyright © 2011 John Wiley & Sons, Ltd.