A multigrid algorithm for the p-Laplacian

We introduce a full approximation storage (FAS) multigrid algorithm to find the finite element solution for a class of nonlinear monotone elliptic pro blems. Since the solution of the problem is equivalent to minimize a strict ly convex functional, we use a Polak-Ribiere conjugate gradient method as t he nonlinear smoother in our algorithm. The advantage in so doing is that w e do not have to calculate derivatives of operators. We prove local converg ence of our algorithm and illustrate its performance by solving benchmark p roblems.