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.
CITATION STYLE
Arndt, D., Braack, M., & Lube, G. (2016). Finite elements for the Navier-Stokes problem with outflow condition. In Lecture Notes in Computational Science and Engineering (Vol. 112, pp. 95–103). Springer Verlag. https://doi.org/10.1007/978-3-319-39929-4_10
Mendeley helps you to discover research relevant for your work.