Classical Residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or references) 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 mat be also to assess the effectivity of the former estimate and to improve it.
Abstract
Classical Residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or references) error. Lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs. This work introduces a [...]
Two implicit residual type estimators yielding upper bounds of the error are presented which do not require flux equilibration. One of them is based on the ideas introduced in [MAC 00, CAR 99, MOR 03, PRU 02]. The new approach introduced here is based on using the estimated error function rather than the estimated error norms. Once the upper bounds are computed, also lower bounds for the error are obtained with little supplementary effort.
Abstract
Two implicit residual type estimators yielding upper bounds of the error are presented which do not require flux equilibration. One of them is based on the ideas introduced in [MAC 00, [...]
Recovering lower bounds of the error postprocessing implicit residual a posteriori error estimates 