A Robust Multigrid Method for Isogeometric Analysis using Boundary Correction

The fast solution of linear systems arising from an isogeometric discretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid solver is naively applied to a linear system arising from an isogeometric discretization, the convergence rates deteriorate significantly if the spline degree is increased. Recently, a robust approximation error estimate and a corresponding inverse inequality for B-splines of maximum smoothness have been shown, both with constants independent of the spline degree. In the present paper, we use these results to construct a multigrid solver for discretizations based on B-splines with maximum smoothness which exhibits robust convergence rates.