ABSTRACT
The multigrid method discussed by Brandt (1977) can be applied directly to solve nonlinear elliptic partial differential equations. Unfortunately, this method is beyond the scope of this text. Any serious effort to solve nonlinear elliptic PDEs should consider the multigrid method very seriously. It works equally well for linear and nonlinear PDEs and for one-, two-, or three-space dimensions. The book by Hackbusch (1980) presents a comprehensive discussion of the multigrid method.
