Analysis of a multilevel iterative method for nonlinear finite element equations
Randolph E. Bank, Donald J. Rose · Mathematics of Computation · 1982
The multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations. We describe how this technique can be combined with a globally convergent approximate Newton method to solve nonlinear partial differential equations. We show that asymptotically only one Newton iteration per level is required; thus the complexity for linear and nonlinear problems is essentially equal.