Properties of triangulations obtained by the longest-edge bisection

被引：4

作者：

Perdomo, Francisco ^{[1
]}

Plaza, Angel

机构：

[1] Univ Las Palmas Gran Canaria, Div Math Graph & Computat MAGiC, IUMA, Las Palmas Gran Canaria 35017, Spain

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2014年 / 12卷 / 12期

关键词：

Triangulation; Longest-edge bisection; Mesh refinement; Mesh regularity; Finite element method; MESH QUALITY IMPROVEMENT; FASTER CONVERGENCE; NON-DEGENERACY; TRIANGLES; PARTITIONS; REGULARITY; ALGORITHM; SCHEME; SIDE;

D O I：

10.2478/s11533-014-0448-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.

引用

页码：1796 / 1810

页数：15

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