Penalty-Factor-Free Stabilized Nonconforming Finite Elements for Solving Stationary Navier-Stokes Equations
Year: 2022
Author: Linshuang He, Minfu Feng, Qiang Ma
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 5 : pp. 728–755
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2101-m2020-0156
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 5 : pp. 728–755
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Stationary Navier-Stokes equations Nonconforming nite elements Penalty stabilization methods DG methods Locally divergence-free.