A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems Original Research Article

This paper presents a non-intrusive method which yields strict and high-quality error bounds of calculated quantities of interest in structural problems solved by the finite element method. The focus is on linear viscoelasticity problems described through internal variables. In order to solve the adjoint problem in a non-intrusive way, we use handbook techniques involving enrichment functions introduced through the partition of unity method (PUM). Then, the mesh and operators used to calculate the reference problem can be reused. Such a procedure also enables one to address error estimation on pointwise quantities of interest, although this implies dealing with infinite-energy Green functions.