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Volume 19, Issue 5
A Least-Squares Stabilization Virtual Element Method for the Stokes Problem on Polygonal Meshes

Yang Li, Chaolang Hu & Minfu Feng

Int. J. Numer. Anal. Mod., 19 (2022), pp. 685-708.

Published online: 2022-08

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  • Abstract

This paper studies the virtual element method for Stokes problem with a least-squares type stabilization. The method cannot only circumvent the Babuška-Brezzi condition, but also make use of general polygonal meshes, as opposed to more standard triangular grids. Moreover, it is suitable for arbitrary combinations of the velocity and pressure, including equal-order virtual element. We obtain the corresponding energy norm error estimates and $L^2$ norm error estimates for velocity. Finally, a series of numerical experiments are performed to verify the method has good behaviors.

  • Keywords

Virtual element method, Stokes problem, Least-squares stabilization.

  • AMS Subject Headings

65N12, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-685, author = {Li , YangHu , Chaolang and Feng , Minfu}, title = {A Least-Squares Stabilization Virtual Element Method for the Stokes Problem on Polygonal Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {5}, pages = {685--708}, abstract = {

This paper studies the virtual element method for Stokes problem with a least-squares type stabilization. The method cannot only circumvent the Babuška-Brezzi condition, but also make use of general polygonal meshes, as opposed to more standard triangular grids. Moreover, it is suitable for arbitrary combinations of the velocity and pressure, including equal-order virtual element. We obtain the corresponding energy norm error estimates and $L^2$ norm error estimates for velocity. Finally, a series of numerical experiments are performed to verify the method has good behaviors.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20935.html} }
TY - JOUR T1 - A Least-Squares Stabilization Virtual Element Method for the Stokes Problem on Polygonal Meshes AU - Li , Yang AU - Hu , Chaolang AU - Feng , Minfu JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 685 EP - 708 PY - 2022 DA - 2022/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20935.html KW - Virtual element method, Stokes problem, Least-squares stabilization. AB -

This paper studies the virtual element method for Stokes problem with a least-squares type stabilization. The method cannot only circumvent the Babuška-Brezzi condition, but also make use of general polygonal meshes, as opposed to more standard triangular grids. Moreover, it is suitable for arbitrary combinations of the velocity and pressure, including equal-order virtual element. We obtain the corresponding energy norm error estimates and $L^2$ norm error estimates for velocity. Finally, a series of numerical experiments are performed to verify the method has good behaviors.

Li , YangHu , Chaolang and Feng , Minfu. (2022). A Least-Squares Stabilization Virtual Element Method for the Stokes Problem on Polygonal Meshes. International Journal of Numerical Analysis and Modeling. 19 (5). 685-708. doi:
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