TY - JOUR
T1 - A Weak Galerkin Finite Element Method for the Navier-Stokes Equations
AU - Jiachuan Zhang, Kai Zhang, Jingzhi Li & Xiaoshen Wang
JO - Communications in Computational Physics
VL - 3
SP - 706
EP - 746
PY - 2018
DA - 2018/03
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0267
UR - https://global-sci.org/intro/article_detail/cicp/10545.html
KW - Weak Galerkin, finite element method, the Navier-Stokes equations.
AB - <p style="text-align: justify;">In this paper, a weak Galerkin finite element method (WGFEM) is proposed
for solving the Navier-Stokes equations (NSEs). The existence and uniqueness of the
WGFEM solution of NSEs are established. The WGFEM provides very accurate numerical
approximations for both the velocity field and pressure field, even with very
high Reynolds numbers. The salient feature is that the flexibility of the WGFEM for
the choice of the order of the velocity and pressure comparing to the standard finite element
methods. Optimal order error estimates in both |·|<sub>$W_h$&nbsp;</sub>and $L^2$ norms are proved
for the semi-discretized scheme. Numerical simulations are presented to show the
efficiency of the WGFEM.</p>