A Remark on Newest Vertex Bisection in Any Space Dimension

Dietmar Gallistl; Mira Schedensack; Rob P. Stevenson

doi:10.1515/cmam-2014-0013

Published by De Gruyter May 1, 2014

A Remark on Newest Vertex Bisection in Any Space Dimension

Dietmar Gallistl , Mira Schedensack and Rob P. Stevenson

From the journal Computational Methods in Applied Mathematics

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

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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 T∈𝒯is 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

Funding source: DFG Research Center Matheon

Funding source: Berlin Mathematical School

Received: 2014-4-22

Accepted: 2014-4-27

Published Online: 2014-5-1

Published in Print: 2014-7-1

A Remark on Newest Vertex Bisection in Any Space Dimension

Abstract.

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