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C\(_{0}\)P\(_{2}\)–P\(_{0}\) Stokes finite element pair on sub-hexahedron tetrahedral grids

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Abstract

This paper presents a procedure to construct stable \(C_0P_2{-}P_0\) finite element pair for three dimensional incompressible Stokes problem. It is proved that, the quadratic-constant finite element pair, though not stable in general, is uniformly stable on a certain family of tetrahedral grids, namely some kind of sub-hexahedron tetrahedral grids. The sub-hexahedron tetrahedral grid is defined by refining each eight-vertex hexahedron of a certain hexahedral grid into twelve tetrahedra with one added vertex inside the hexahedron, while the hexahedral grid is a partition of a polyhedral domain where each (non-flat face) hexahedron is defined by a tri-linear mapping on the unit cube with eight vertices.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Shangyou Zhang

  2. LSEC, ICMSEC and NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shuo Zhang

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  1. Shangyou Zhang
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  2. Shuo Zhang
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Correspondence to Shuo Zhang.

Additional information

The work is supported by National Centre for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences. The first author is partially supported by the National Natural Science Foundation of China (NSFC) Project 11571023. The second author is partially supported by the NSFC Project 11471026.

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Zhang, S., Zhang, S. C\(_{0}\)P\(_{2}\)–P\(_{0}\) Stokes finite element pair on sub-hexahedron tetrahedral grids. Calcolo 54, 1403–1417 (2017). https://doi.org/10.1007/s10092-017-0235-2

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  • DOI: https://doi.org/10.1007/s10092-017-0235-2

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