WIAS Preprint No. 1671, (2011)

Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection


  • Galvin, Keith
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Rebholz, Leo
  • Wilson, Nicholas

2010 Mathematics Subject Classification

  • 76D05 76M10


  • mixed finite elements, incompressible Navier-Stokes equations, poor mass conservation, grad-div stabilization, natural convection, Scott-Vogelius element




We consider the problem of poor mass conservation in mixed finite element algorithms for flow problems with large rotation-free forcing in the momentum equation. We provide analysis that suggests for such problems, obtaining accurate solutions necessitates either the use of pointwise divergence-free finite elements (such as Scott-Vogelius), or heavy grad-div stabilization of weakly divergence-free elements. The theory is demonstrated in numerical experiments for a benchmark natural convection problem, where large irrotational forcing occurs with high Rayleigh numbers.

Appeared in

  • Comput. Methods Appl. Mech. Engrg., 237--240 (2012) pp. 166--176.

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