Generalized Prager–Synge identity and robust equilibrated error estimators for discontinuous elements

The well-known Prager–Synge identity is valid in H1(Ω) and serves as a foundation for developing equilibrated posteriori error estimators continuous elements. In this paper, we introduce new identity, that may be regarded generalization of the to piecewise functions diffusion problems. For nonconforming finite element approximation arbitrary odd order, improve current methods by proposing fully explicit approach recovers an flux H(div;Ø) through local element-wise scheme. efficiency recovered robust with respect coefficient jump regardless its distribution. discontinuous elements, note typical recovering H1 function can proved only under some restrictive assumptions. To promote unconditional robustness estimator jump, propose recover gradient H(curl;Ω) space simple averaging technique over facets. Our resulting globally reliable locally efficient Nevertheless, reliability constant no longer 1.