Adv. Appl. Math. Mech., 17 (2025), pp. 1625-1653.
Published online: 2025-09
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0281}, url = {http://global-sci.org/intro/article_detail/aamm/24489.html} }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.