Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems

Abstract

In this work, we set up a non-intrusive procedure that yields for strict and high-quality error bounds of quantities of interest in linear viscoelasticity problems solved by means of the finite element method (FEM). The goal-oriented error estimation approach uses the concept of dissipation error and classical duality techniques involving the solution of an adjoint problem. The non-intrusive feature of this approach is achieved by introducing enrichment functions, via a partition of unity, when solving the adjoint problem numerically (handbook techniques), so that the discretization parameters defined for the primal problem can be reused. The resulting local error estimation method is thus highly effective, easy to implement in a finite element code, and it enables to consider discretization error on truly pointwise quantities of interest.