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In this paper we review the hypercircle method of Prager and Synge. Thistheory inspired several studies and induced an active research in the area of aposteriori error analysis. In particular, we review the Braess--Sch\"oberlerror estimator in the context of the Poisson problem. We discuss adaptivefinite element schemes based on two variants of the estimator and we prove theconvergence and optimality of the resulting algorithms.

The Prager-Synge theorem in reconstruction based a posteriori error estimation