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Generalization of the Zlámal condition for simplicial finite elements in ℝd

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Abstract

The famous Zlámal’s minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in 2d. In this paper we present and discuss its generalization to simplicial partitions in any space dimension.

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Authors and Affiliations

  1. Korteweg-de Vries Institute, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands

    Jan Brandts

  2. BCAM—Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, E-48160, Derio, Basque Country, Spain

    Sergey Korotov

  3. IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain

    Sergey Korotov

  4. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67, Prague 1, Czech Republic

    Michal Křížek

Authors
  1. Jan Brandts
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  2. Sergey Korotov
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  3. Michal Křížek
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Corresponding author

Correspondence to Jan Brandts.

Additional information

The second author was partially supported by Grant MTM2008-03541 of the MICINN, Spain, the ERC Advanced Grant FP7-246775 NUMERIWAVES and Grant PI2010-04 of the Basque Government. The third author was supported by Grant no. IAA 100190803 of the Grant Agency of the Academy of Sciences of the Czech Republic and the Institutional Research Plan AV0Z 10190503.

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Brandts, J., Korotov, S. & Křížek, M. Generalization of the Zlámal condition for simplicial finite elements in ℝd . Appl Math 56, 417–424 (2011). https://doi.org/10.1007/s10492-011-0024-1

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  • DOI: https://doi.org/10.1007/s10492-011-0024-1

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