Uniform Convergence Estimates for Multigrid
V-cycle Algorithms with Less than Full Elliptic Regularity

J. H. Bramble
Department of Mathematics
Cornell University
Ithaca, NY 14853

J. E. Pasciak
Applied Math Department
Brookhaven National Laboratory
Upton, NY 11973


In this paper, we provide uniform estimates for V-cycle algorithms with one smoothing on each level. This theory is based on some elliptic regularity but does not require a smoother interaction hypothesis (sometimes referred to as a strengthened Cauchy Schwarz inequality) assumed in other theories. Thus, it is a natural extension of the full regularity V-cycle estimates provided by Braess and Hackbusch in [2].

Contributed April 2, 1993.