Computable bounds of functional outputs in linear visco-elastodynamics

This work presents a new technique yielding computable bounds of quantities of interest in the framework of linear visco-elastodynamics. A novel expression for the error representation is introduced, alternative to the previous ones using the Cauchy–Schwarz inequality. The proposed formulation utilizes symmetrized forms of the error equations to derive error bounds in terms of energy error measures. The practical implementation of the method is based on constructing admissible fields for both the original problem and the adjoint problem associated with the quantity of interest. Here, the flux-free technique is considered to compute the admissible stress fields. The proposed methodology yields estimates with better quality than the ones based on the Cauchy–Schwarz inequality. In the studied examples the bound gaps obtained are approximately halved, that is the estimated intervals of confidence are reduced.

► We introduce new computable bounds for quantities of interest in linear visco-elastodynamics.
► The derivation of the alternative strategy makes no use of Cauchy–Schwarz inequality.
► The practical implementation requires the standard construction of the admissible fields.
► Better quality estimates are found in all numerical experiments (halved bound gap).
► As for the previous approaches, the estimates deteriorate as the viscosity goes to zero.