  We develop a multigrid solver for the second biharmonic problem in the
context of Isogeometric Analysis (IgA), where we also allow a zero-order term.
In a previous paper, the authors have developed an analysis for the first
biharmonic problem based on Hackbusch's framework. This analysis can only be
extended to the second biharmonic problem if one assumes uniform grids. In this
paper, we prove a multigrid convergence estimate using Bramble's framework for
multigrid analysis without regularity assumptions. We show that the bound for
the convergence rate is independent of the scaling of the zero-order term and
the spline degree. It only depends linearly on the number of levels, thus
logarithmically on the grid size. Numerical experiments are provided which
illustrate the convergence theory and the efficiency of the proposed multigrid
approaches.
