Title:       Smoothers, mesh dependent norms, interpolation 
             and multigrid

Author:      Susanne C. Brenner

Published:   Applied Numerical Mathematics 
             v. 43 (2002),  45-56

Abstract:    New estimates for the nodal interpolation operator for 
             the $P_1$ finite element are established with respect to
             mesh dependent norms that are defined in terms of the 
             smoothers in multigrid algorithms.  These estimates are 
             useful in the additive approach to the convergence of
             $V$-cycle multigrid algorithms and lead to results on
             the asymptotic behavior of the contraction numbers with 
             respect to the number of smoothing steps.