Error estimation for the HHT method in non-linear solid dynamics

This work presents a new error estimator that can be used in both linear and non-linear solid and structural dynamic problems. Specifically, this estimator is developed for the Hilber–Hughes–Taylor (HHT) method and it takes into account the error made in displacements and velocities. Since the accelerations computed by the HHT method are not sufficiently accurate to be used in the estimator, a strategy is presented to compute new accelerations with a minor computational cost. Finally, an efficient implementation of the estimator is designed.