@Article{JCM-26-456,
author = {Shangyou Zhang},
title = {On the $P_1$ Powell-Sabin Divergence-Free Finite Element for the Stokes Equations},
journal = {Journal of Computational Mathematics},
year = {2008},
volume = {26},
number = {3},
pages = {456--470},
abstract = {<p style="text-align: justify;">The stability of the $P_1$-$P_0$ mixed-element &nbsp; is established on general Powell-Sabin triangular grids. &nbsp;The piecewise linear finite element solution approximating &nbsp; the velocity is divergence-free pointwise &nbsp; for the Stokes equations. &nbsp;The finite element solution approximating the pressure in &nbsp; the Stokes equations can be obtained as a byproduct if &nbsp; an iterative method is adopted for solving the discrete &nbsp; linear system of equations. &nbsp;Numerical tests are presented confirming the theory on the stability and the optimal order of convergence for the $P_1$ Powell-Sabin &nbsp; divergence-free finite element method.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8636.html}
}