(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
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 "arbitrary-order" polynomials, and stability is guaranteed by the "absolutely stabilized finite element formulation" 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.