WIAS Preprint No. 1835, (2013)

Improving efficiency of coupled schemes for Navier--Stokes equations by a connection to grad-div stabilized projection methods


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

2010 Mathematics Subject Classification

  • 76D05 65M60


  • incompressible Navier-Stokes equations, projection method, grad-div stabilization, divergence-free finite elements




We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin/Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter γ, converge to the associated coupled method solution with rate γ-1 as γ → ∞. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters can dramatically improve accuracy.

Appeared in

  • J. Numer. Math., 25 (2017), pp. 229--248, DOI 10.1515/jnma-2016-1024 ; changed title: A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier--Stokes equations.

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