Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows

Gert Lube; Daniel Arndt; Helene Dallmann

doi:10.1007/978-3-319-25727-3_12

Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows

Gert Lube, Daniel Arndt, Helene Dallmann

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

5 Scopus citations

Abstract

The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.

Original language	English
Title of host publication	Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
Editors	Petr Knobloch
Publisher	Springer Verlag
Pages	147-169
Number of pages	23
ISBN (Print)	9783319257259
DOIs	https://doi.org/10.1007/978-3-319-25727-3_12
State	Published - 2015
Externally published	Yes
Event	Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014 - Prague, Czech Republic Duration: Sep 15 2014 → Sep 19 2014

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	108
ISSN (Print)	1439-7358

Conference

Conference	Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
Country/Territory	Czech Republic
City	Prague
Period	09/15/14 → 09/19/14

Funding

The work of Daniel Arndt was supported by CRC 963 founded by German research council (DFG). The work of Helene Dallmann was supported by the RTG 1023 founded by German research council (DFG)

Funders	Funder number
Deutsche Forschungsgemeinschaft	RTG 1023

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10.1007/978-3-319-25727-3_12

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Lube, G., Arndt, D., & Dallmann, H. (2015). Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows. In P. Knobloch (Ed.), Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014 (pp. 147-169). (Lecture Notes in Computational Science and Engineering; Vol. 108). Springer Verlag. https://doi.org/10.1007/978-3-319-25727-3_12

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abstract = "The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.",

author = "Gert Lube and Daniel Arndt and Helene Dallmann",

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Lube, G, Arndt, D & Dallmann, H 2015, Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows. in P Knobloch (ed.), Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014. Lecture Notes in Computational Science and Engineering, vol. 108, Springer Verlag, pp. 147-169, Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014, Prague, Czech Republic, 09/15/14. https://doi.org/10.1007/978-3-319-25727-3_12

Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows. / Lube, Gert; Arndt, Daniel; Dallmann, Helene.
Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014. ed. / Petr Knobloch. Springer Verlag, 2015. p. 147-169 (Lecture Notes in Computational Science and Engineering; Vol. 108).

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

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AB - The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.

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Understanding the limits of inf-sup stable galerkin-FEM for incompressible flows

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