On some new recovery based a posteriori error estimators ∗ G. Maisano a , S. Micheletti b , S. Perotto b , C.L. Bottasso a,1 a Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy b MOX - Modeling and Scientific Computing, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy Abstract 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. Key words: Recovery techniques; A posteriori analysis; Error estimators; Finite elements ∗ Contract/grant sponsor: COFIN 2003 “Numerical Models for Advanced Applica- tions in Fluid Dynamics and Electromagnetism” Email addresses: giorgio.maisano@polimi.it (G. Maisano), stefano.micheletti@mate.polimi.it (S. Micheletti), simona.perotto@mate.polimi.it (S. Perotto), carlo.bottasso@polimi.it (C.L. Bottasso). 1 Correspondence to: C.L. Bottasso, Dipartimento di Ingegneria Aerospaziale, Po- litecnico di Milano, Via La Masa 34, 20156 Milano, Italy. Preprint submitted to CMAME 21 July 2005