PENALTY-FACTOR-FREE STABILIZED NONCONFORMING FINITE ELEMENTS FOR SOLVING STATIONARY NAVIER-STOKES EQUATIONS  

作　　者：Linshuang He Minfu Feng Qiang Ma 

机构地区：[1]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Journal of Computational Mathematics》2022年第5期728-755,共28页计算数学（英文）

基　　金：National Nature Science Foundation of China(No.11971337,No.11801387)。

摘　　要：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 P1 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.

关 键 词：Stationary Navier-Stokes equations Nonconforming finite elements Penalty stabilization methods DG methods Locally divergence-free. 

分 类 号：O17[理学—数学]