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

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

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.

Author Details

Yu Xiong

Yanping Chen

Jianwei Zhou

Qin Liang

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