Year: 2024
Author: Yu Xiong, Yanping Chen, Jianwei Zhou, Qin Liang
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 1 : pp. 210–242
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0071
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 1 : pp. 210–242
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Optimal error estimates divergence-free virtual element nonlinear damping term.