In this paper, we extend the divergence-free VEM of [L. Beirão da Veiga, C. Lovadina and G. Vacca, Virtual elements for the Navier-Stokes problem on polygonal meshes, SIAM J. Numer. Anal. 56 (2018) 1210-1242] to the Oseen problem, including a suitable stabilization procedure that guarantees robustness in the convection-dominated case without disrupting the divergence-free property. The stabilization is inspired from [N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzman, A. Linke and C. Merdon, A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation, SIAM J. Numer. Anal. 59 (2021) 2746-2774] and includes local SUPG-like terms of the vorticity equation, internal jump terms for the velocity gradients, and an additional VEM stabilization. We derive theoretical convergence results that underline the robustness of the scheme in different regimes, including the convection-dominated case. Furthermore, as in the non-stabilized case, the influence of the pressure on the velocity error is moderate, as it appears only through higher-order terms.

Beirão da Veiga, L., Dassi, F., Vacca, G. (2022). Vorticity-stabilized virtual elements for the Oseen equation. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 31(14), 3009-3052 [10.1142/S0218202521500688].

Vorticity-stabilized virtual elements for the Oseen equation

Beirão da Veiga, L.;Dassi, F.;
2022

Abstract

In this paper, we extend the divergence-free VEM of [L. Beirão da Veiga, C. Lovadina and G. Vacca, Virtual elements for the Navier-Stokes problem on polygonal meshes, SIAM J. Numer. Anal. 56 (2018) 1210-1242] to the Oseen problem, including a suitable stabilization procedure that guarantees robustness in the convection-dominated case without disrupting the divergence-free property. The stabilization is inspired from [N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzman, A. Linke and C. Merdon, A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation, SIAM J. Numer. Anal. 59 (2021) 2746-2774] and includes local SUPG-like terms of the vorticity equation, internal jump terms for the velocity gradients, and an additional VEM stabilization. We derive theoretical convergence results that underline the robustness of the scheme in different regimes, including the convection-dominated case. Furthermore, as in the non-stabilized case, the influence of the pressure on the velocity error is moderate, as it appears only through higher-order terms.
Articolo in rivista - Articolo scientifico
convection-dominated problems; Oseen equation; polygonal meshes; Virtual elements;
English
3009
3052
44
Beirão da Veiga, L., Dassi, F., Vacca, G. (2022). Vorticity-stabilized virtual elements for the Oseen equation. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 31(14), 3009-3052 [10.1142/S0218202521500688].
Beirão da Veiga, L; Dassi, F; Vacca, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/352499
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