Analysis of error estimators for the semidiscrete equations of linear solid and structural dynamics

An analysis is presented of the errors made in the time integration of the semidiscrete equations of linear solid and structural dynamics. The analysis addresses the relation between local and global errors in the time integration, setting forward the necessary and sufficient conditions for the formulation of valid error estimates of a general class. The same analysis reveals the limitations of some error estimators when the external loading is not smooth. Also, a new simple error estimator is proposed that shows improved estimation accuracy in problems with rough solutions.