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2016 | OriginalPaper | Chapter

Finite Elements for the Navier-Stokes Problem with Outflow Condition

Authors : Daniel Arndt, Malte Braack, Gert Lube

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2015

Publisher: Springer International Publishing

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Abstract

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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Metadata
Title
Finite Elements for the Navier-Stokes Problem with Outflow Condition
Authors
Daniel Arndt
Malte Braack
Gert Lube
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-39929-4_10

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