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Inventory Control Under Parametric Uncertainty of Underlying Models Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Convergence Speed of Generalized Longest-Edge-Based Refinement

Authors : José P. Suárez, Tania Moreno, Pilar Abad, Ángel Plaza

Published in: IAENG Transactions on Engineering Technologies

Publisher: Springer Netherlands

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Abstract

In the refinement of meshes, one wishes to iteratively subdivide a domain following geometrical partition rules. The aim is to obtain a new discretized domain with adapted regions. We prove that the Longest Edge \(n\)-section of triangles for \(n\geqslant 4\) produces a finite sequence of triangle meshes with guaranteed convergence of diameters and review previous result when \(n\) equals 2 and 3. We give upper and lower bounds for the convergence speed in terms of diameter reduction. Then we fill the gap in the analysis of the diameters convergence for generalized Longest Edge based refinement. In addition, we give a numerical study for the case of \(n=4\), the so-called LE quatersection, evidencing its utility in adaptive mesh refinement.

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Metadata
Title
Convergence Speed of Generalized Longest-Edge-Based Refinement
Authors
José P. Suárez
Tania Moreno
Pilar Abad
Ángel Plaza
Copyright Year
2013
Publisher
Springer Netherlands
Book
IAENG Transactions on Engineering Technologies

Print ISBN: 978-94-007-6189-6

Electronic ISBN: 978-94-007-6190-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-6190-2_39