A Safeguarded Zienkiewicz-Zhu Estimator

A hybrid a posteriori error estimator for conforming finite element approximations

“…Recovery-based estimators, e.g., the Zienkiewicz-Zhu (ZZ) estimator and its variations (cf. [34,35,27,13,21,8,18], etc. ), are quite popular in the engineering community.…”

“…[3,10]). For linear elements, [18,17] adds two additional terms (one of them is the element residual) to the ZZ estimator to ensure reliability on coarse meshes. For higher order elements, however, a straightforward extension of the original ZZ estimator [34,35] usually fails and developing a viable estimator is nontrivial.…”