Finite Elements for the Navier-Stokes Problem with Outflow Condition
- Cite this paper as:
- Arndt D., Braack M., Lube G. (2016) Finite Elements for the Navier-Stokes Problem with Outflow Condition. In: Karasözen B., Manguoğlu M., Tezer-Sezgin M., Göktepe S., Uğur Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham
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.