Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations  

作　　者：Gang Chen Xiaoping Xie 

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

出　　处：《Science China Mathematics》2024年第5期1133-1158,共26页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12171341 and 11801063);supported by National Natural Science Foundation of China(Grant Nos.12171340 and 11771312);the Fundamental Research Funds for the Central Universities(Grant No.YJ202030)。

摘　　要：In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the P_(k)/P_(k-1)(k≥1)discontinuous finite element combination for the velocity and pressure approximations in the interior of elements,piecewise Pm(m=k,k-1)for the velocity gradient approximation in the interior of elements,and piecewise P_(k)/P_(k) for the trace approximations of the velocity and pressure on the inter-element boundaries.We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size.Based on the derived discrete HDG Sobolev embedding properties,optimal error estimates are obtained.Numerical experiments are performed to verify the theoretical analysis.

关 键 词：Navier-Stokes equations HDG methods DIVERGENCE-FREE uniqueness condition error estimates 

分 类 号：O241.82[理学—计算数学]