On the convergence rate of grad-div stabilized Taylor--Hood to Scott--Vogelius solutions for incompressible flow problems
- Linke, Alexander
- Rebholz, Leo G.
- Wilson, Nicholas E.
2010 Mathematics Subject Classification
- 65M60 65N30 76D05
- Navier-Stokes equations, Scott-Vogelius, Taylor-Hood, strong mass conservation, MHD, Leray-alpha
It was recently proven 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 $gamma^-frac12$ (where $gamma$ is the stabilization parameter), the computational results suggest the rate may be improvable $gamma^-1$. We prove herein the analytical rate is indeed $gamma^-1$, and extend the result to other incompressible flow problems including Leray-$alpha$ and MHD. Numerical results are given that verify the theory.
- J. Math. Anal. Appl., 381 (2011) pp. 612--626.