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Title: Convergence of longest edge n-section of triangles
Authors: Suárez, Jose P. 
Moreno, Tania
Abad, Pilar 
Plaza, Ángel 
UNESCO Clasification: 120603 Análisis de errores
Keywords: Longest-edge
Mesh refinement
Triangle partition
Issue Date: 2012
Journal: Lecture notes in engineering and computer science 
Conference: 2012 World Congress on Engineering, WCE 2012 
Abstract: Let t be a triangle in R2. We find the Longest Edge (LE) of t, insert n−1 equally-space points in the LE and connect them to the opposite vertex. This yields the generation of n new sub-triangles whose parent is t. Now, continue this process iteratively. Proficient algorithms for mesh refinement using this method are known when n = 2, but less known when n = 3 and completely unknown when n 4. We prove that the LE n-section of triangles for n 4 of triangles produces a finite sequence of triangle meshes with guaranteed convergence of diameters. 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 general Longest Edge based subdivision. 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.
ISBN: 9789881925213
ISSN: 2078-0958
Source: World Congress on Engineering, WCE 2012; Imperial College LondonLondon; United Kingdom; 4 July 2012 through 6 July 2012 [ISSN 2078-0958], v. 2198, p. 869-873
Appears in Collections:Actas de congresos
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