Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems

In this paper, we aim at extending to stochastic models a general and robust goal-oriented error estimation method presented in previous works. This method, which is based on the constitutive relation error and classical extraction techniques, enables to obtain strict bounds on quantities of interest. In the stochastic framework, several aspects are revisited in the current paper: (i) the construction of admissible fields, which is a pillar of the constitutive relation error; (ii) the error bounding itself; (iii) the splitting of error sources that may enable to drive adaptive procedures effectively. Performances of the proposed approach are illustrated on two-dimensional applications.