On some new recovery-based a posteriori error estimators

The paper is concerned with the formulation of recovery-based a posteriori error estimators. At first we analyze a variant of the well-known Zienkiewicz–Zhu method, which is here formulated so as to be exact in one dimension for quadratic solutions on non-uniform grids. Next, we discuss two methods which operate directly on the solution, rather than its gradient: one is based on a solution enrichment using the Zienkiewicz–Zhu recovered gradient, while the other consists of a roughening of the solution followed by a Zienkiewicz–Zhu-like recovery. The three new proposed methods are compared in terms of their effectivity indices and solution accuracy to the Zienkiewicz–Zhu estimator, and are applied to representative two- and three-dimensional problems.