A simple analysis of some a posteriori error estimates

Abstract We analyze two popular classes of a posteriori error estimates within the abstract framework established by Babuska 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.

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