  In this paper, we will construct and analyze a multigrid algorithm that can
be applied to weighted H(div)-problems on a two-dimensional domain. These
problems arise after performing a dimension reduction to a three-dimensional
axisymmetric H(div)-problem. We will use recently developed Fourier finite
element spaces that can be applied to axisymmetric H(div)-problems with general
data. We prove that if the axisymmetric domain is convex, then the multigrid
V-cycle with modern smoothers will converge uniformly with respect to the
meshsize.
