@Article{JCM-38-310,
author = {Zhang , BaijuYang , Yan and Feng , Minfu},
title = {A $C^0$-Weak Galerkin Finite Element Method for the Two-Dimensional Navier-Stokes Equations in Stream-Function Formulation},
journal = {Journal of Computational Mathematics},
year = {2020},
volume = {38},
number = {2},
pages = {310--336},
abstract = {<p style="text-align: justify;">We propose and analyze a $C^0$-weak Galerkin (WG) finite element method for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied. The proposed method uses continuous piecewise-polynomial approximations of degree $k+2$ for the stream-function $\psi$ and discontinuous piecewise-polynomial approximations of degree $k+1$ for the trace of $\nabla\psi$ on the interelement boundaries. The existence of a discrete solution is proved by means of a topological degree argument, while the uniqueness is obtained under a data smallness condition. An optimal error estimate is obtained in $L^2$-norm, $H^1$-norm and broken $H^2$-norm. Numerical tests are presented to demonstrate the theoretical results.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1806-m2017-0287},
url = {http://global-sci.org/intro/article_detail/jcm/14519.html}
}