Sharp polynomial dependence of the boundary-strip contraction

Determine whether the true contraction rate of the exact boundary-strip patch sweep has polynomial dependence on the polynomial degree p, accounting for coupling accumulated across the boundary strip rather than only the worst single-patch estimate.

Background

The paper proves that the boundary-strip contraction factor is uniformly bounded below one with respect to the mesh level and cut configuration for each fixed polynomial degree. However, the resulting estimates have superexponential dependence on p, primarily through the ghost-energy comparison factor. Numerical experiments suggest that repeated cut-strip sweeps mitigate the deterioration, but the experiments do not determine the asymptotic dependence of the exact strip contraction. The authors explicitly leave open whether the true rate is only polynomial in p.