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Inf-sup stable non-conforming finite elements of arbitrary order on triangles

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Abstract

We introduce a family of scalar non-conforming finite elements of arbitrary order k≥1 with respect to the H1-norm on triangles. Their vector-valued version generates together with a discontinuous pressure approximation of order k−1 an inf-sup stable finite element pair of order k for the Stokes problem in the energy norm. For k=1 the well-known Crouzeix-Raviart element is recovered.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780, Bochum, Germany

    Gunar Matthies

  2. Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39106, Magdeburg, Germany

    Lutz Tobiska

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  1. Gunar Matthies
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  2. Lutz Tobiska
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Correspondence to Gunar Matthies.

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Matthies, G., Tobiska, L. Inf-sup stable non-conforming finite elements of arbitrary order on triangles. Numer. Math. 102, 293–309 (2005). https://doi.org/10.1007/s00211-005-0648-8

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  • DOI: https://doi.org/10.1007/s00211-005-0648-8

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