A Remark on Newest Vertex Bisection in Any Space Dimension

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 T′ of a conforming partition T in which one simplex has been bisected. In this note, we show that the difference in levels between any T′∈T′ and its ancestor T∈T is uniformly bounded. This result has been used in Lemma 4.2 of [SIAM J. Numer. Anal. 51 (2013), 2935-2955] by Carstensen and the first two authors. Keywords: Newest-Vertex Bisection; Adaptive Mesh-Refinement; n-Simplice