Finite Elements for the Navier-Stokes Problem with Outflow Condition
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.
- 2.Y. Bazilevs, J. Gohean, T. Hughes, R. Moser, Y. Zhang, Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput. Methods Appl. Mech. Eng. 198 (45), 3534–3550 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 3.M. Braack, Outflow condition for the Navier–Stokes equations with skew-symmetric formulation of the convective term, in BAIL 2014. Lecture Notes in Computational Science and Engineering (Springer, Cham, 2016), pp. 35–45Google Scholar
- 7.H. Dallmann, Finie element methods with local projection stabilization for thermally coupled incompressible flow, Ph.D. thesis, University of Göttingen, 2015Google Scholar