1. Robust optimal multilevel preconditioners for non-conforming finite element systems<FNR></FNR><FN>Dedicated to Professor Owe Axelsson on the occasion of his 70th birthday, with respect and appreciation </FN>. Author Blaheta, R., Margenov, S., and Neytcheva, M. Subjects *FINITE element method, *NUMERICAL analysis, *MATHEMATICAL analysis, *MATHEMATICS, *LINEAR systems Abstract We consider strategies to construct optimal order two- and multilevel hierarchical preconditioners for linear systems as arising from the finite element discretization of self-adjoint second order elliptic problems using non-conforming Crouzeix–Raviart linear elements. In this paper we utilize the hierarchical decompositions, derived in a previous work by the same authors (Numerical Linear Algebra with Applications 2004; 11:309–326) and provide a further analysis of these decompositions in order to assure robustness with respect to anisotropy. Finally, we show how to construct both multiplicative and additive versions of the algebraic multilevel iteration preconditioners and show robustness and optimal order convergence estimates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2005 Full Text View/download PDF