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A Comparison of Simplicial and Block Finite Elements

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Numerical Mathematics and Advanced Applications 2009

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Abstract

In this note we discuss and compare the performance of the finite element method (FEM) on two popular types of meshes – simplicial and block ones. A special emphasis is put on the validity of discrete maximum principles and on associated (geometric) mesh generation/refinement issues in higher dimensions. As a result, we would recommend to carefully reconsider the common belief that the simplicial finite elements are very convenient to describe complicated geometries (which appear in real-life problems), and also that the block finite elements, due to their simplicity, should be used if the geometry of the solution domain allows that.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Tampere University of Technology, 553, FI–33101, Tampere, Finland

    Sergey Korotov

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

    Tomáš Vejchodský

Authors
  1. Sergey Korotov
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  2. Tomáš Vejchodský
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Corresponding author

Correspondence to Sergey Korotov .

Editor information

Editors and Affiliations

  1. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Gunilla Kreiss

  2. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Per Lötstedt

  3. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Axel Målqvist

  4. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Maya Neytcheva

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Korotov, S., Vejchodský, T. (2010). A Comparison of Simplicial and Block Finite Elements. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_57

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