\documentclass{ws-p8-50x6-00}
\title{
Multilevel HB Preconditioning of Non-Conforming FEM Systems
}
\author{ Tzanio V. Kolev and Svetozar D. Margenov
}
\date{}
\begin{document}

\maketitle

\abstracts{
In this paper we present a framework of a multilevel hierarchical basis (HB)
preconditioning of non-conforming FEM systems for second order elliptic
boundary value problems.
The Crouzeix-Raviart linear finite elements are implemented to the
numerical solution of the problem. A pure algebraic multiplicative
preconditioner is constructed based on a proper hierarchical basis of the FEM
discretization space. Let us remind, that the nodal FEM spaces corresponding to
successive levels of mesh refinements are not nested in the case of such
non-conforming elements.
The convergence of the related PCG iterative method is illustrated by
numerical tests for model large-scale problems.

\bigskip \\
{\bf Key words:} PCG, multilevel preconditioners, non-conforming FEM
\\
{\bf AMS subject classifications:} 65F10, 65N30
}

\end{document}