A lowest-order divergence-free virtual element method for Navier-Stokes equations with damping on polygonal mesh

作     者：Chen, Yanping Li, Qing Huang, Jian Xiong, Yu 

作者机构：School of Mathematics and Computational Science Xiangtan University & National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 China School of Science Nanjing University of Posts and Telecommunications Nanjing 210023 China 

出 版 物：《Journal of Mathematical Analysis and Applications》 (J. Math. Anal. Appl.)

年 卷 期：2025年第552卷第2期

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China, NSFC, (12426616) National Natural Science Foundation of China, NSFC Nanjing University of Posts and Telecommunications, NUPT, (NY223127) Nanjing University of Posts and Telecommunications, NUPT National Key Research and Development Program of China, NKRDPC, (2024YFA1012600) National Key Research and Development Program of China, NKRDPC Xiangtan University, XTU, (XDCX2024Y178) Xiangtan University, XTU Science and Technology Program of Hunan Province, (2024RC3159) Science and Technology Program of Hunan Province 

主　　题：Divergence-free Lowest-order virtual element Navier-Stokes equations with damping Polygonal mesh Pressure-independent velocity error estimate 

摘      要：This paper focuses on designing a lowest-order divergence-free virtual element method for solving Navier-Stokes equations with a nonlinear damping term on polygonal meshes. The exact divergence-free property of virtual space preserves the mass-conservation of the system. With the application of Helmholtz projection, we provide stability estimates regarding the velocity. An optimal convergence estimate is derived, showing that the error estimate for the velocity in energy norm is pressure-independent. Finally, we perform various numerical simulations to validate the accuracy of our theoretical findings. © 2025 Elsevier Inc.