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Calcolo
Erschienen in: Calcolo 4/2017

17.08.2017

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

verfasst von: Shangyou Zhang, Shuo Zhang

Erschienen in: Calcolo | Ausgabe 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.
Vorheriger Artikel An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions
Nächster Artikel A fully discrete scheme for the pressure–stress formulation of the time-domain fluid–structure interaction problem

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Metadaten
Titel
CP–P Stokes finite element pair on sub-hexahedron tetrahedral grids
verfasst von
Shangyou Zhang
Shuo Zhang
Publikationsdatum
17.08.2017
Verlag
Springer Milan
Erschienen in
Calcolo / Ausgabe 4/2017
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-017-0235-2

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