TY - JOUR T1 - Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes AU - Xiong , Yu AU - Chen , Yanping AU - Zhou , Jianwei AU - Liang , Qin JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 210 EP - 242 PY - 2024 DA - 2024/02 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0071 UR - https://global-sci.org/intro/article_detail/nmtma/22916.html KW - Optimal error estimates, divergence-free, virtual element, nonlinear damping term. AB -

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 $\mathbf{H}^1$-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 convergence 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.