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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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1609-9389
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Volume 14, Issue 3

Issues

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
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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' 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 T𝒯 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-Simplices

MSC: 65N50; 65Y20; 65N30

About the article

Received: 2014-04-22

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, DOI: https://doi.org/10.1515/cmam-2014-0013.

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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
C. Carstensen and H. Rabus
SIAM Journal on Numerical Analysis, 2017, Volume 55, Number 6, Page 2644
[2]
Alex Bespalov, Alexander Haberl, and Dirk Praetorius
Computer Methods in Applied Mechanics and Engineering, 2017, Volume 317, Page 318

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