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On angle conditions in the finite element nethod

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Abstract

Angle conditions play an important role in the analysis of the finite element method. They enable us to derive the optimal interpolation order and prove convergence of this method, to derive various a posteriori error estimates, to perform regular mesh refinements, etc. In 1968, Miloš Zlámal introduced the minimum angle condition for triangular elements. From that time onward many other useful geometric angle conditions on the shape of elements appeared. In this paper, we shall give a survey of various generalizations of the minimum and also maximum angle condition in the finite element method and present some of their applications.

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Authors and Affiliations

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

    Jan Brandts

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

    Antti Hannukainen

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

    Sergey Korotov

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

    Michal Křîžek

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

    Michal Křîžek

Authors
  1. Jan Brandts
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  2. Antti Hannukainen
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  3. Sergey Korotov
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  4. Michal Křîžek
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Correspondence to Jan Brandts.

Additional information

Dedicated to Prof. Martin Stynes on his 60th birthday

The third author was 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 fourth author was supported by the 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., Hannukainen, A., Korotov, S. et al. On angle conditions in the finite element nethod. SeMA 56, 81–95 (2011). https://doi.org/10.1007/BF03322598

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