New Nonlinear Multigrid Analysis

Dexuan Xie
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, NY 10012


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.

Contributed June 4, 1997.