Locally adapted tetrahedral meshes using bisection

D. N. Arnold, A. Mukherjee, L. Pouly

Research output: Contribution to journalArticlepeer-review

137 Scopus citations


We present an algorithm for the construction of locally adapted conformal tetrahedral meshes. The algorithm is based on bisection of tetrahedra. A new data structure is introduced, which simplifies both the selection of the refinement edge of a tetrahedron and the recursive refinement to conformity of a mesh once some tetrahedra have been bisected. We prove that repeated application of the algorithm leads to only finitely many tetrahedral shapes up to similarity, and we bound the amount of additional refinement that is needed to achieve conformity. Numerical examples of the effectiveness of the algorithm are presented.

Original languageEnglish (US)
Pages (from-to)431-448
Number of pages18
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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