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Stability of the 8-tetrahedra shortest-interior-edge partitioning method

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Abstract

We consider a tetrahedron partitioning method, known in the literature as the 8-tetrahedra shortest-interior-edge partition. For this method, which is a variant of Freudenthal’s algorithm in three space dimensions, we prove that the infinite series of refined meshes (for any given initial mesh) is stable in the sense that the degree of degeneracy of the cells remains bounded. We give an explicit estimate in terms of a standard shape quality measure introduced by Liu and Joe. Furthermore, we show that our estimate is sharp. The estimate also holds for Freudenthal’s algorithm (in three space dimensions) provided that it is initialized appropriately. Numerical experiments confirm our result as well as its sharpness.

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Authors and Affiliations

  1. Center for Complex Systems and Visualization, University of Bremen, Universitätsallee 29, 28359, Bremen, Germany

    Tim Kröger & Tobias Preusser

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  1. Tim Kröger
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  2. Tobias Preusser
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Correspondence to Tim Kröger.

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Kröger, T., Preusser, T. Stability of the 8-tetrahedra shortest-interior-edge partitioning method. Numer. Math. 109, 435–457 (2008). https://doi.org/10.1007/s00211-008-0148-8

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  • DOI: https://doi.org/10.1007/s00211-008-0148-8

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