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 eld can be global or local (probing the chosen quantity in a speci c 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 di erent approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost-e ciency. A well-known numerical example, the Cook’s membrane, is used for the numerical evaluations