  In this paper we review the hypercircle method of Prager and Synge. This
theory inspired several studies and induced an active research in the area of a
posteriori error analysis. In particular, we review the Braess--Sch\"oberl
error estimator in the context of the Poisson problem. We discuss adaptive
finite element schemes based on two variants of the estimator and we prove the
convergence and optimality of the resulting algorithms.
