Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes  

作　　者：Yu Xiong Yanping Chen Jianwei Zhou Qin Liang 

机构地区：[1]School of Mathematics and Computational Science,Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105,P.R.China [2]School of Mathematics and Statistics Linyi University,Linyi 276005,P.R.China [3]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期210-242,共33页高等学校计算数学学报（英文版）

摘　　要：In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and exact divergence-free.By virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete scheme.The con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the pressure.Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.

关 键 词：Optimal error estimates DIVERGENCE-FREE virtual element nonlinear damping term. 

分 类 号：O17[理学—数学]