Finite Elements for the Navier-Stokes Problem with Outflow Condition

  • Daniel Arndt
  • Malte BraackEmail author
  • Gert Lube
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 112)


This work is devoted to the Directional Do-Nothing (DDN) condition as an outflow boundary condition for the incompressible Navier-Stokes equation. In contrast to the Classical Do-Nothing (CDN) condition, we have stability, existence of weak solutions and, in the case of small data, also uniqueness. We derive an a priori error estimate for this outflow condition for finite element discretizations with inf-sup stable pairs. Stabilization terms account for dominant convection and the divergence free constraint. Numerical examples demonstrate the stability of the method.


Weak Solution Outflow Boundary Projection Error Outflow Condition Piecewise Constant Approximation 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of GöttingenGöttingenGermany
  2. 2.Mathematical SeminarUniversity of KielKielGermany

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