TY - JOUR
T1 - The Lowest-Order Stabilized Virtual Element Method for the Stokes Problem
AU - Liu , Xin
AU - Song , Qixuan
AU - Gao , Yu
AU - Chen , Zhangxin
JO - Communications in Computational Physics
VL - 1
SP - 221
EP - 247
PY - 2024
DA - 2024/07
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0233
UR - https://global-sci.org/intro/article_detail/cicp/23302.html
KW - Stokes equations, stabilized virtual element scheme, pressure jump, pressure projection, polygonal meshes.
AB - <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>