  In recent publications, the author and his coworkers have shown robust
approximation error estimates for B-splines of maximum smoothness and have
proposed multigrid methods based on them. These methods allow to solve the
linear system arizing from the discretization of a partial differential
equation in Isogeometric Analysis in a single-patch setting with convergence
rates that are provably robust both in the grid size and the spline degree. In
real-world problems, the computational domain cannot be nicely represented by
just one patch. In computer aided design, such domains are typically
represented as a union of multiple patches. In the present paper, we extend the
approximation error estimates and the multigrid solver to this multi-patch
case.
