WIAS Preprint No. 2132, (2015)

On spurious oscillations due to irrotational forces in the Navier--Stokes momentum balance


  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Merdon, Christian
    ORCID: 0000-0002-3390-2145

2010 Mathematics Subject Classification

  • 76D05 76M10

2008 Physics and Astronomy Classification Scheme

  • 47.11.Fg


  • incompressible Navier--Stokes equations, mixed finite element methods, benchmarks, spurious velocity oscillations




This contribution studies the influence of the pressure on the velocity error in finite element discretisations of the Navier--Stokes equations. Three simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. For widely used finite element methods like the Taylor--Hood finite element method, such relatively large pressures can lead to spurious oscillations and arbitrarily large errors in the velocity, even if the exact velocity is in the ansatz space. Only mixed finite element methods, whose velocity error is pressure-independent, like the Scott--Vogelius finite element method can avoid this influence.

Appeared in

  • J. Comput. Phys., 313 (2016) pp. 654--661.

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