On faster convergence of the bisection method for all triangles
Author: Martin Stynes
Journal: Math. Comp. 35 (1980), 1195-1201
MSC: Primary 51N99; Secondary 65B99, 65N30
MathSciNet review: 583497
Abstract: Let be a triangle with vertices A, B, and C. It is "bisected" as follows: choose a/the longest side (say AB) of , let D be the midpoint of AB, then replace by two triangles and .
Let be a given triangle. Bisect into two triangles and . Next bisect each , forming four new triangles . Continue thus, forming an infinite sequence , of sets of triangles, where . Let denote the mesh of . It is shown that there exists such that, for , , thus greatly improving the previous best known bound of .
It is also shown that only a finite number of distinct shapes occur among the triangles produced, and that, as the method proceeds, tends to become covered by triangles which are approximately equilateral in a certain sense.
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