## Abstract

First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the criterion function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a sequence of conforming nested simplicial meshes whose shape is determined by the mesh density function. We prove that the corresponding mesh size of the sequence tends to zero for d∈=∈2, 3 as the bisection algorithm proceeds. It is also demonstrated numerically that the algorithm seems to produce only a finite number of similarity-distinct triangles.

Original language | English |
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Title of host publication | Large-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers |

Pages | 571-579 |

Number of pages | 9 |

Volume | 5910 LNCS |

DOIs | |

Publication status | Published - 2010 |

MoE publication type | A4 Article in a conference publication |

Event | International Conference on Large-Scale Scientific Computations - Sozopol, Bulgaria Duration: 4 Jun 2009 → 8 Jun 2009 Conference number: 7 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5910 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Conference

Conference | International Conference on Large-Scale Scientific Computations |
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Abbreviated title | LSSC |

Country | Bulgaria |

City | Sozopol |

Period | 04/06/2009 → 08/06/2009 |