On Error Analysis for the 3D Navier-Stokes Equations in Velocity-Vorticity-Helicity Form

We present a rigorous numerical analysis and computational tests for the Galerkin finite element discretization of the velocity-vorticity-helicity formulation of the equilibrium Navier-Stokes equations (NSE). This formulation was recently derived by the authors, is the first NSE formulation that directly solves for helicity, the first velocityvorticity formulation to naturally enforce incompressibility of the vorticity, and preliminary computations confirm its potential. We present a numerical scheme, prove stability, existence of solutions, uniqueness under a small data condition, convergence, and provide numerical experiments to confirm the theory and illustrate the effectiveness of the scheme on a benchmark problem.