Strategies for computing goal‐oriented a posteriori error measures in non‐linear elasticity

We investigate the characteristics and performance of goal‐oriented a posteriori error measures for a class of non‐linear elasticity models, while restriction is made to small strain theory. The chosen error measure of the displacement field can be global or local (probing the chosen quantity in a specific spatial point). The error is computable with the aid of the solution of a dual problem whose data depend on the error measure. The main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost‐efficiency. A well‐known numerical example, the Cook's membrane, is used for the numerical evaluations.