- Journal Home
- Volume 36 - 2024
- Volume 35 - 2024
- Volume 34 - 2023
- Volume 33 - 2023
- Volume 32 - 2022
- Volume 31 - 2022
- Volume 30 - 2021
- Volume 29 - 2021
- Volume 28 - 2020
- Volume 27 - 2020
- Volume 26 - 2019
- Volume 25 - 2019
- Volume 24 - 2018
- Volume 23 - 2018
- Volume 22 - 2017
- Volume 21 - 2017
- Volume 20 - 2016
- Volume 19 - 2016
- Volume 18 - 2015
- Volume 17 - 2015
- Volume 16 - 2014
- Volume 15 - 2014
- Volume 14 - 2013
- Volume 13 - 2013
- Volume 12 - 2012
- Volume 11 - 2012
- Volume 10 - 2011
- Volume 9 - 2011
- Volume 8 - 2010
- Volume 7 - 2010
- Volume 6 - 2009
- Volume 5 - 2009
- Volume 4 - 2008
- Volume 3 - 2008
- Volume 2 - 2007
- Volume 1 - 2006
Commun. Comput. Phys., 36 (2024), pp. 221-247.
Published online: 2024-07
Cited by
- BibTex
- RIS
- TXT
In this paper, we develop and analyze two stabilized mixed virtual element schemes for the Stokes problem based on the lowest-order velocity-pressure pairs (i.e., a piecewise constant approximation for pressure and an approximation with an accuracy order $k = 1$ for velocity). By applying local pressure jump and projection stabilization, we ensure the well-posedness of our discrete schemes and obtain the corresponding optimal $H^1$- and $L^2$-error estimates. The proposed schemes offer a number of attractive computational properties, such as, the use of polygonal/polyhedral meshes (including non-convex and degenerate elements), yielding a symmetric linear system that involves neither the calculations of higher-order derivatives nor additional coupling terms, and being parameter-free in the local pressure projection stabilization. Finally, we present the matrix implementations of the essential ingredients of our stabilized virtual element methods and investigate two- and three-dimensional numerical experiments for incompressible flow to show the performance of these numerical schemes.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0233}, url = {http://global-sci.org/intro/article_detail/cicp/23302.html} }In this paper, we develop and analyze two stabilized mixed virtual element schemes for the Stokes problem based on the lowest-order velocity-pressure pairs (i.e., a piecewise constant approximation for pressure and an approximation with an accuracy order $k = 1$ for velocity). By applying local pressure jump and projection stabilization, we ensure the well-posedness of our discrete schemes and obtain the corresponding optimal $H^1$- and $L^2$-error estimates. The proposed schemes offer a number of attractive computational properties, such as, the use of polygonal/polyhedral meshes (including non-convex and degenerate elements), yielding a symmetric linear system that involves neither the calculations of higher-order derivatives nor additional coupling terms, and being parameter-free in the local pressure projection stabilization. Finally, we present the matrix implementations of the essential ingredients of our stabilized virtual element methods and investigate two- and three-dimensional numerical experiments for incompressible flow to show the performance of these numerical schemes.