A Multigrid Algorithm for Nonlinear Monotone Elliptic Problems

R. Bermejo and J.A. Infante


Abstract

We introduce a FAS multigrid algorithm to find the finite element solution for a class of nonlinear monotone elliptic problems. Since the solution of the problem is equivalent to minimize a strictly convex functional, we use Polak-Ribiere conjugate gradient method as the nonlinear smoother in our algorithm. The advantage in so doing is that we do not have to calculate derivatives of operators. We prove the convergence of our algorithm and illustrate its performance by solving benchmark problems.