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

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外文摘要：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 Pk/Pk-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 Pk/Pk 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.

外文关键词：

Navier-Stokes equationsHDG methodsdivergence-freeuniqueness conditionerror estimates

作者：

Gang Chen、Xiaoping Xie

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作者单位：

School of Mathematics,Sichuan University,Chengdu 610064,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaFundamental Research Funds for the Central UniversitiesNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

项目编号：

1217134111801063YJ2020301217134011771312

出版年：

2024

DOI：

10.1007/s11425-022-2077-7

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(5)