Vorticity-stabilized virtual elements for the Oseen equation

  • Beirão da Veiga, Lourenco (University Milano Bicocca)
  • Dassi, Franco (University Milano Bicocca)
  • Vacca, Giuseppe (University of Bari)

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In this talk we consider Oseen problems in a convection-dominated regime. To solve this kind of partial differential equation, we combine the virtual element divergence-free discretisation shown in Beirão da Veiga et al. 2018 and the stabilisation approach proposed in N. Ahmed et al. 2021. Such a stabilisation is based on SUPG-like terms of the vorticity equation and internal jump terms for the velocity gradients and it was properly adapted for the virtual element framework. We will provide some theoretical convergence results that underline both the robustness of the scheme in different regimes and the low influence of pressure on the velocity error. Finally, we will show some numerical results that validate the theory also from a numerical point of view.