## Abstract

An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, together with some other observations, are used to describe restrictions on the local combinatorial structure of simplicial meshes in which every simplex is well-centered. In particular, it is shown that in a 3-well-centered (2-well-centered) tetrahedral mesh there are at least 7 (9) edges incident to each interior vertex, and these bounds are sharp. Moreover, it is shown that, in stark contrast to the 2-dimensional analog, where there are exactly two vertex links that prevent a well-centered triangle mesh in R^{2}, there are infinitely many vertex links that prohibit a well-centered tetrahedral mesh in R^{3}.

Original language | English (US) |
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Pages (from-to) | 700-724 |

Number of pages | 25 |

Journal | Computational Geometry: Theory and Applications |

Volume | 46 |

Issue number | 6 |

DOIs | |

State | Published - Aug 1 2013 |

## Keywords

- Acute triangulations
- Circumcentric dual
- Discrete exterior calculus
- Finite element method
- Mesh generation

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics