On the $P_1$ Powell-Sabin Divergence-Free Finite Element for the Stokes Equations

On the $P_1$ Powell-Sabin Divergence-Free Finite Element for the Stokes Equations

Year:    2008

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 3 : pp. 456–470

Abstract

The stability of the $P_1$-$P_0$ mixed-element   is established on general Powell-Sabin triangular grids.  The piecewise linear finite element solution approximating   the velocity is divergence-free pointwise   for the Stokes equations.  The finite element solution approximating the pressure in   the Stokes equations can be obtained as a byproduct if   an iterative method is adopted for solving the discrete   linear system of equations.  Numerical tests are presented confirming the theory on the stability and the optimal order of convergence for the $P_1$ Powell-Sabin   divergence-free finite element method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2008-JCM-8636

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 3 : pp. 456–470

Published online:    2008-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Powell Sabin triangles Mixed finite elements Stokes Divergence-free element.