A simple analysis of some a posteriori error estimates Original Research Article

We analyze two popular classes of a posteriori error estimates within the abstract framework established by Babuška and Aziz (1972). Within this framework, we find that bounds for the a posteriori error estimates depend on several of the same constants as a priori error estimates, notably the famous inf—sup constant. We apply our general theory to some specific finite element approximations for the Poisson equation and Stokes equations.