On the convergence rate of grad-div stabilized Taylor–Hood to Scott–Vogelius solutions for incompressible flow problems

It was recently proven in Case et al. (2010) [2] that, under mild restrictions, grad-div stabilized Taylor–Hood solutions of Navier–Stokes problems converge to the Scott–Vogelius solution of that same problem. However, even though the analytical rate was only shown to be γ − 1 2 (where γ is the stabilization parameter), the computational results suggest the rate may be improvable to γ − 1 . We prove herein the analytical rate is indeed γ − 1 , and extend the result to other incompressible flow problems including Leray-α and MHD. Numerical results are given that verify the theory.