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17-08-2017

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

Authors: Shangyou Zhang, Shuo Zhang

Published in: Calcolo | Issue 4/2017

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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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Title: CP–P Stokes finite element pair on sub-hexahedron tetrahedral grids
Authors: Shangyou Zhang
Shuo Zhang
Publication date: 17-08-2017
Publisher: Springer Milan
Published in: Calcolo / Issue 4/2017
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-017-0235-2

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