Bounded flatness in \(Q\)-triangulated regular \(n\)-simplexes. (English) Zbl 0914.65057
Summary: 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 \((\lfloor (n+1)/2 \rfloor)^{n/2} \cdot F^r_n\), where \(F^r_n\) is the flatness of the regular unit \(n\)-simplex.
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
Software:
SimplicialVIEWReferences:
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