V-cycle convergence for non-inherited CutFEM forms

Establish a mesh- and cut-uniform V-cycle convergence bound for geometric multigrid with vertex-patch smoothing applied to CutFEM discretizations whose level forms are non-inherited, using BPX-type machinery.

Background

The paper establishes a two-level convergence result and a conditional W-cycle result under the smallness assumption that the two-level rate is at most one quarter. The numerical experiments use the stronger V-cycle, but the analysis does not cover it because rediscretized, non-inherited level forms require a different multilevel framework. The authors explicitly identify a V-cycle bound as unresolved.