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The maximum angle condition is not necessary for convergence of the finite element method

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Abstract

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π.

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Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Antti Hannukainen

  2. BCAM, Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, 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, Žitná 25, 115 67, Prague 1, Czech Republic

    Michal Křížek

Authors
  1. Antti Hannukainen
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  2. Sergey Korotov
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  3. Michal Křížek
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Corresponding author

Correspondence to Sergey Korotov.

Additional information

Dedicated to Prof. Qun Lin on his 75th birthday.

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Hannukainen, A., Korotov, S. & Křížek, M. The maximum angle condition is not necessary for convergence of the finite element method. Numer. Math. 120, 79–88 (2012). https://doi.org/10.1007/s00211-011-0403-2

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  • DOI: https://doi.org/10.1007/s00211-011-0403-2

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