Before revision:  Here  , we derive an a posteriori error estimator based on the dual weighted residual method that allows for a splitting of the error into averaging error, error on the slow scale and error on the fast scale.
After revision:  Here , we generalize this multiscale approach to a larger class of problems but in particular , we derive an a posteriori error estimator based on the dual weighted residual method that allows for a splitting of the error into averaging error, error on the slow scale and error on the fast scale.