On the stability of the PPH subdivision scheme on nonuniform grids

Abstract

Our purpose in this article is to prove the stability of the subdivision scheme associated with the PPH reconstruction on nonuniform grids. This subdivision scheme is convexity preserving and therefore quite interesting from the practical point of view. Therefore, it is also of utmost importance to count with a stability result ensuring its applicability in real cases. The theoretical stability has been proven for $3-local$ $\sigma$ quasi-uniform grids with $\sigma \le 3\sqrt{5}-5.$ In the numerical experiments we analyze the sharpness of the given stability bound and of the restriction on the grids.