Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier-Stokes flows
Provides theoretical guarantees for divergence-free FEM in unsteady Navier-Stokes, addressing a known bottleneck in pressure robustness for fluid dynamics simulations.
The authors prove pressure-robust and Reynolds-number-robust velocity error estimates for a conforming divergence-free FEM for evolutionary Navier-Stokes flows, with numerical validation on vortex and boundary layer problems.
This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the velocity that hold independently of both pressure and Reynolds number. Here, a key aspect is the use of the discrete Stokes projection for the error splitting. Optionally, edge-stabilisation can be included in the case of dominant convection. Emphasising the importance of conservation properties, the theoretical results are complemented with numerical simulations of vortex dynamics and laminar boundary layer flows.