TY - JOUR
T1 - Penalty-Factor-Free Stabilized Nonconforming Finite Elements for Solving Stationary Navier-Stokes Equations
AU - He , Linshuang
AU - Feng , Minfu
AU - Ma , Qiang
JO - Journal of Computational Mathematics
VL - 5
SP - 728
EP - 755
PY - 2022
DA - 2022/05
SN - 40
DO - http://doi.org/10.4208/jcm.2101-m2020-0156
UR - https://global-sci.org/intro/article_detail/jcm/20545.html
KW - Stationary Navier-Stokes equations, Nonconforming nite elements, Penalty stabilization methods, DG methods, Locally divergence-free.
AB - <p style="text-align: justify;">Two nonconforming penalty methods for the two-dimensional stationary Navier-Stokes equations are studied in this paper. These methods are based on the weakly continuous $P_1$ vector fields and the locally divergence-free (LDF) finite elements, which respectively penalize local divergence and are discontinuous across edges. These methods have no penalty factors and avoid solving the saddle-point problems. The existence and uniqueness of the velocity solution are proved, and the optimal error estimates of the energy norms and $L^2$-norms are obtained. Moreover, we propose unified pressure recovery algorithms and prove the optimal error estimates of $L^2$-norm for pressure. We design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis.</p>