A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements

Date

2015-07-01

Author

Belenli, Mine Akbas
Rebholz, Leo G.
Tone, Florentina

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We prove a long-time stability result for the finite element in space, linear extrapolated Crank-Nicolson in time discretization of the Navier-Stokes equations (NSE). From this result and a numerical experiment, we show the importance of discrete mass conservation in long-time simulations of the NSE. That is, we show that using elements that strongly enforce mass conservation can provide significantly more accurate solutions over long times, compared to those that enforce it weakly.

Subject Keywords

Navier-Stokes equations, Long-time stability, Divergence-free finite elements, Crank-Nicolson

URI

https://hdl.handle.net/11511/67101

Journal

APPLIED MATHEMATICS LETTERS

DOI

https://doi.org/10.1016/j.aml.2015.01.018

Collections

Department of Mathematics, Article

Citation Formats

M. A. Belenli, L. G. Rebholz, and F. Tone, “A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements,” APPLIED MATHEMATICS LETTERS, vol. 45, pp. 98–102, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67101.