Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates

Classical residual type error estimators approximate the error ux around the elements and yield upper bounds of the exact (or reference) error. Lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs. This work introduces a simple and cheap strategy to recover a lower bound estimate from standard upper bound estimates. This lower bound may also be used to assess the e ectivity of the former estimate and to improve it