@Article{CiCP-36-1,
author = {Xin, Liu and Song, Qixuan and Yu, Gao and Zhangxin, Chen},
title = {The Lowest-Order Stabilized Virtual Element Method for the Stokes Problem},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {1},
pages = {221--247},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0233},
url = {https://global-sci.com/article/90905/the-lowest-order-stabilized-virtual-element-method-for-the-stokes-problem}
}