New stabilized P₁ × P₀ finite element methods for nearly inviscid and incompressible flows

This work proposes a new stabilized P₁×P₀ finite element method for solving the incompressible Navier–Stokes equations. The numerical scheme is based on a reduced Bernardi–Raugel element with statically condensed face bubbles and is pressure-robust in the small viscosity regime. For the Stokes problem, an error estimate uniform with respect to the kinematic viscosity is shown. For the Navier–Stokes equation, the nonlinear convection term is discretized using an edge-averaged finite element method. In comparison with classical schemes, the proposed method does not require tuning of parameters and is validated for competitiveness on several benchmark problems in 2 and 3 dimensional space.