Effective postprocessing for equilibration a posteriori error estimators

Guaranteed error control via fully discrete a posteriori error estimators is possible with typical overestimation between 1.25 and 2 in simple computer benchmarks. The equilibration techniques due to Braess and that due to Luce–Wohlmuth are efficient tools with an accuracy limited by the hyper-circle threshold. This motivates postprocessing strategies and the analysis of successive improvements of guaranteed upper error bounds with a few pcg iterations result in reduced overestimation factors between 1 and 1.25. Numerical simulations for three classes of applications illustrate the efficiency for the Poisson model problem with and without jumping coefficients or a simple obstacle problem.