WIAS Preprint No. 1589, (2011)

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



Authors

  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Rebholz, Leo G.
  • Wilson, Nicholas E.

2010 Mathematics Subject Classification

  • 65M60 65N30 76D05

Keywords

  • Navier-Stokes equations, Scott-Vogelius, Taylor-Hood, strong mass conservation, MHD, Leray-alpha

Abstract

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.

Appeared in

  • J. Math. Anal. Appl., 381 (2011) pp. 612--626.

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