@Article{JCM-40-5,
author = {Linshuang, He and Minfu, Feng and Qiang, Ma},
title = {Penalty-Factor-Free Stabilized Nonconforming Finite Elements for Solving Stationary Navier-Stokes Equations},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {5},
pages = {728--755},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2101-m2020-0156},
url = {https://global-sci.com/article/84200/penalty-factor-free-stabilized-nonconforming-finite-elements-for-solving-stationary-navier-stokes-equations}
}