Year: 2026
Type: preprint
Abstract: On triangular meshes, we analyze local mesh refinement based on longest-edge bisection equipped with the serial longest-edge propagation-path closure. Ties are resolved by terminal priority: if the incoming shared edge is a longest edge of the neighboring triangle, the pair is declared terminal and that edge is bisected. For every adaptive mesh sequence $\mathcal{T}_0, \mathcal{T}_1, \ldots, \mathcal{T}_L$ with a sequence of marked sets $\mathcal{M}_0, \mathcal{M}_1, \ldots, \mathcal{M}_{L-1}$, we prove the cumulative closure estimate $$\#\mathcal{T}_L-\#\mathcal{T}_0 \lesssim\sum_{\ell=0}^{L-1}\#\mathcal{M}_\ell.$$ The proof derives single-mark locality from the uniform multiplicative gap between possible descendant diameters implied by finite similarity classes, and converts this locality into the cumulative estimate through a Binev--Dahmen--DeVore-type charging argument.
Source: arXiv (Cornell University)
Authors: Li, Yuwen, Yang, Zhiyuan
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208722826