A methodology for the formulation of error estimators for time integration in linear solid and structural dynamics

In this article, we present a novel methodology for the formulation of a posteriori error estimators applicable to time-stepping algorithms of the type commonly employed in solid and structural mechanics. The estimators constructed with the presented methodology are accurate and can be implemented very efficiently. More importantly, they provide reliable error estimations even in non-smooth problems where many standard estimators fail to capture the order of magnitude of the error. The proposed methodology is applied, as an illustrative example, to construct an error estimator for the Newmark method. Numerical examples of its performance and comparison with existing error estimators are presented. These examples verify the good accuracy and robustness predicted by the a