New Nonlinear Multigrid Analysis

                                  Dexuan Xie
                 Courant Institute of Mathematical Sciences,
                             New York University,
                              251 Mercer Street,
                             New York, NY 10012,
                             dexuan@cims.nyu.edu


                                   Abstract

The nonlinear multigrid method is an efficient algorithm for solving the
system of nonlinear equations arising from the numerical discretization of
nonlinear elliptic boundary problems.  In this paper, we present a new
nonlinear multigrid analysis as an extension of the linear multigrid theory
presented by Bramble et al.  In particular, we prove the convergence of the
nonlinear V-cycle method for a class of mildly nonlinear second order elliptic
boundary value problems which do not have full elliptic regularity.  Numerical
examples are presented to investigate the influence of different choices of
the two auxiliary parameters of the nonlinear V-cycle method to the
convergence.