Bounded flatness in Q-triangulated regular N-simplexes

摘要

Bounded flatness of simplexes is crucial for simplicial algorithms to provide solutions of satisfactory accuracy. By using combinatorial arguments we show that iterative Q-refinement with arbitrary mesh of Euclidean simplexes, a crucial step in the implementation of simplicial algorithms, yields subsimplexes of bounded flatness. The flatness is bounded by (⌞(n + 1)2⌟)n/2 · Fnr, where Fnr is the flatness of the regular unit n-simplex.