On the Prager–Synge method for a posteriori error

The classic method by Prager and Synge (“hypercircle” method) for a posteriori error estimation in addressed from the viewpoint of the extension of the applicability domain (the range of analyzed problems and methods of the realization). The nonintrusive version of the approximation error estimation that implements the method by Prager and Synge for the arbitrary PDE system is presented. The semiheuristical variant of the Prager and Synge method may be related with the modern approaches for approximation error estimation on the ensemble of solutions obtained by the algorithms of different inner structure.