TY - JOUR
T1 - An Absolutely Stabilized Virtual Element Method for  the Incompressible Stokes Equations
AU - Zhang , Xi
AU - Feng , Minfu
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1625
EP - 1653
PY - 2025
DA - 2025/09
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0281
UR - https://global-sci.org/intro/article_detail/aamm/24489.html
KW - Absolutely stabilized mixed VEM, incompressible Stokes equation, arbitrary-order polynomials.
AB - <p style="text-align: justify;">In this paper, we propose an absolutely stabilized mixed virtual element
 method (mixed VEM) for the incompressible Stokes equations. We employ the $C^0$-conforming virtual element space for the velocity and discontinuous polynomial space
 for the pressure. The velocity-pressure pair contains&quot;arbitrary-order&quot; polynomials,
 and stability is guaranteed by the&quot;absolutely stabilized finite element formulation&quot; originally introduced in [21]. We establish error estimates in the energy norm for both
 velocity and pressure, as well as an $L^2-$ error estimate for the velocity. Several numerical experiments validate the theoretical analysis.</p>