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.
Díez, P.; Pares, N.; Huerta, A. Accurate upper and lower error bounds by solving flux-free local problems in "stars". "Revue européenne des élements finis", Desembre 2004, vol. 13, núm. 5-6-7, p. 497-507.