Journal
NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS (ENUMATH 2015)
Volume 112, Issue -, Pages 95-103Publisher
SPRINGER INT PUBLISHING AG
DOI: 10.1007/978-3-319-39929-4_10
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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.
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