Finite elements for the Navier-Stokes problem with outflow condition

Daniel Arndt; Malte Braack; Gert Lube

doi:10.1007/978-3-319-39929-4_10

Finite elements for the Navier-Stokes problem with outflow condition

Daniel Arndt, Malte Braack, Gert Lube

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

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.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2015
Editors	Murat Manguoglu, Bulent Karasozen, Munevver Tezer-Sezgin, Omur Ugur, Munevver Tezer-Sezgin, Murat Manguoglu, Omur Ugur, Serdar Goktepe, Omur Ugur, Munevver Tezer-Sezgin, Murat Manguoglu, Bulent Karasozen, Bulent Karasozen, Serdar Goktepe, Serdar Goktepe
Publisher	Springer Verlag
Pages	95-103
Number of pages	9
ISBN (Print)	9783319399270, 9783319399270, 9783319399270
DOIs	https://doi.org/10.1007/978-3-319-39929-4_10
State	Published - 2016
Externally published	Yes
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015 - Ankara, Turkey Duration: Sep 14 2015 → Sep 18 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	112
ISSN (Print)	1439-7358

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015
Country/Territory	Turkey
City	Ankara
Period	09/14/15 → 09/18/15

Access to Document

10.1007/978-3-319-39929-4_10

Cite this

Arndt, D., Braack, M., & Lube, G. (2016). Finite elements for the Navier-Stokes problem with outflow condition. In M. Manguoglu, B. Karasozen, M. Tezer-Sezgin, O. Ugur, M. Tezer-Sezgin, M. Manguoglu, O. Ugur, S. Goktepe, O. Ugur, M. Tezer-Sezgin, M. Manguoglu, B. Karasozen, B. Karasozen, S. Goktepe, & S. Goktepe (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2015 (pp. 95-103). (Lecture Notes in Computational Science and Engineering; Vol. 112). Springer Verlag. https://doi.org/10.1007/978-3-319-39929-4_10

Arndt, Daniel ; Braack, Malte ; Lube, Gert. / Finite elements for the Navier-Stokes problem with outflow condition. Numerical Mathematics and Advanced Applications ENUMATH 2015. editor / Murat Manguoglu ; Bulent Karasozen ; Munevver Tezer-Sezgin ; Omur Ugur ; Munevver Tezer-Sezgin ; Murat Manguoglu ; Omur Ugur ; Serdar Goktepe ; Omur Ugur ; Munevver Tezer-Sezgin ; Murat Manguoglu ; Bulent Karasozen ; Bulent Karasozen ; Serdar Goktepe ; Serdar Goktepe. Springer Verlag, 2016. pp. 95-103 (Lecture Notes in Computational Science and Engineering).

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title = "Finite elements for the Navier-Stokes problem with outflow condition",

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.",

author = "Daniel Arndt and Malte Braack and Gert Lube",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015 ; Conference date: 14-09-2015 Through 18-09-2015",

year = "2016",

doi = "10.1007/978-3-319-39929-4_10",

language = "English",

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series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

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editor = "Murat Manguoglu and Bulent Karasozen and Munevver Tezer-Sezgin and Omur Ugur and Munevver Tezer-Sezgin and Murat Manguoglu and Omur Ugur and Serdar Goktepe and Omur Ugur and Munevver Tezer-Sezgin and Murat Manguoglu and Bulent Karasozen and Bulent Karasozen and Serdar Goktepe and Serdar Goktepe",

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Arndt, D, Braack, M & Lube, G 2016, Finite elements for the Navier-Stokes problem with outflow condition. in M Manguoglu, B Karasozen, M Tezer-Sezgin, O Ugur, M Tezer-Sezgin, M Manguoglu, O Ugur, S Goktepe, O Ugur, M Tezer-Sezgin, M Manguoglu, B Karasozen, B Karasozen, S Goktepe & S Goktepe (eds), Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol. 112, Springer Verlag, pp. 95-103, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015, Ankara, Turkey, 09/14/15. https://doi.org/10.1007/978-3-319-39929-4_10

Finite elements for the Navier-Stokes problem with outflow condition. / Arndt, Daniel; Braack, Malte; Lube, Gert.
Numerical Mathematics and Advanced Applications ENUMATH 2015. ed. / Murat Manguoglu; Bulent Karasozen; Munevver Tezer-Sezgin; Omur Ugur; Munevver Tezer-Sezgin; Murat Manguoglu; Omur Ugur; Serdar Goktepe; Omur Ugur; Munevver Tezer-Sezgin; Murat Manguoglu; Bulent Karasozen; Bulent Karasozen; Serdar Goktepe; Serdar Goktepe. Springer Verlag, 2016. p. 95-103 (Lecture Notes in Computational Science and Engineering; Vol. 112).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Arndt, Daniel

AU - Braack, Malte

AU - Lube, Gert

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PY - 2016

Y1 - 2016

N2 - 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.

AB - 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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A2 - Karasozen, Bulent

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PB - Springer Verlag

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Arndt D, Braack M, Lube G. Finite elements for the Navier-Stokes problem with outflow condition. In Manguoglu M, Karasozen B, Tezer-Sezgin M, Ugur O, Tezer-Sezgin M, Manguoglu M, Ugur O, Goktepe S, Ugur O, Tezer-Sezgin M, Manguoglu M, Karasozen B, Karasozen B, Goktepe S, Goktepe S, editors, Numerical Mathematics and Advanced Applications ENUMATH 2015. Springer Verlag. 2016. p. 95-103. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-39929-4_10

Finite elements for the Navier-Stokes problem with outflow condition

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