@Article{NMTMA-17-210,
author = {Xiong , YuChen , YanpingZhou , Jianwei and Liang , Qin},
title = {Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {1},
pages = {210--242},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0071 },
url = {http://global-sci.org/intro/article_detail/nmtma/22916.html}
}