A Remark on Newest Vertex Bisection in Any Space Dimension
Dietmar Gallistl, Mira Schedensack, Rob P. Stevenson ยท Computational Methods in Applied Mathematics ยท 2014
Abstract. With newest vertex bisection, there is no uniform bound on the number of n-simplices that need to be refined to arrive at the smallest conforming refinement ๐ฏ ' $\mathcal {T}^{\prime }$ of a conforming partition ๐ฏ $\mathcal {T}$ in which one simplex has been bisected. In this note, we show that the difference in levels between any T ' โ ๐ฏ ' $T^{\prime } \in \mathcal {T}^{\prime }$ and its ancestor T โ ๐ฏ $T \in \mathcal {T}$ is uniformly bounded. This result has been used in Lemma 4.2 of [SIAM J. Numer. Anal. 51 (2013), 2935โ2955] by Carstensen and the first two authors.