  This note describes the full approximation storage (FAS) multigrid scheme for
an easy one-dimensional nonlinear boundary value problem. The problem is
discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles
and F-cycles, with a nonlinear Gauss-Seidel smoother, to solve the resulting
finite-dimensional problem. The mathematics of the FAS restriction and
prolongation operators, in the FE case, are explained. A self-contained Python
program implements the scheme. Optimal performance, i.e. work proportional to
the number of unknowns, is demonstrated for both kinds of cycles, including
convergence nearly to discretization error in a single F-cycle.
