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Red-green refinement of simplicial meshes in $ d$ dimensions

Author: Jörg Grande
Journal: Math. Comp. 88 (2019), 751-782
MSC (2010): Primary 65M50, 65N50, 65D18
Published electronically: October 9, 2018
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Abstract: The local red-green mesh refinement of consistent, simplicial meshes in $ d$ dimensions is considered. We give a constructive solution to the green closure problem in arbitrary dimension $ d$. Suppose that $ \mathcal {T}$ is a simplicial mesh and that $ R$ is an arbitrary subset of its faces, which is refined with the Coxeter-Freudenthal-Kuhn (red) refinement rule. Green refinements of simplices $ S\in \mathcal {T}$ are generated to restore the consistency of the mesh using a particular placing triangulation. No new vertices are created in this process. The green refinements are consistent with the red refinement on $ R$, the unrefined mesh regions, and all other neighboring green refinements.

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Additional Information

Jörg Grande
Affiliation: Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany

Keywords: Local mesh refinement, red--green refinement, green closure, simplicial meshes, Kuhn triangulation
Received by editor(s): November 10, 2016
Received by editor(s) in revised form: January 2, 2018
Published electronically: October 9, 2018
Article copyright: © Copyright 2018 Jörg Grande