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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

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1609-9389
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Volume 14, Issue 3

# A Remark on Newest Vertex Bisection in Any Space Dimension

Dietmar Gallistl
/ Mira Schedensack
/ Rob P. Stevenson
• Korteweg–de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, Netherlands
• Email
• Other articles by this author:
Published Online: 2014-05-01 | DOI: https://doi.org/10.1515/cmam-2014-0013

## 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 ${𝒯}^{\text{'}}$ of a conforming partition $𝒯$ in which one simplex has been bisected. In this note, we show that the difference in levels between any ${T}^{\text{'}}\in {𝒯}^{\text{'}}$ and its ancestor $T\in 𝒯$ 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.

MSC: 65N50; 65Y20; 65N30

Accepted: 2014-04-27

Published Online: 2014-05-01

Published in Print: 2014-07-01

Citation Information: Computational Methods in Applied Mathematics, Volume 14, Issue 3, Pages 317–320, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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© 2014 by Walter de Gruyter Berlin/Boston.