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On angle conditions in the finite element method

  1. 1. 0364798 - MU-W 2012 RIV ES eng J - Journal Article
    Brandts, J. - Hannukainen, A. - Korotov, S. - Křížek, Michal
    On angle conditions in the finite element method.
    Sociedad Espaňola de Matemática Aplicada. Roč. 56, - (2011), s. 81-95. ISSN 1575-9822
    R&D Projects: GA AV ČR(CZ) IAA100190803
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : simplicial finite elements * minimum and maximum angle condition * ball conditions
    Subject RIV: BA - General Mathematics

    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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