A low-degree strictly conservative finite element method for incompressible flows on general triangulations
The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 225-248.

In this study, a new P 2 -P 1 finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn’s inequality hold for general triangulations. It yields strictly conservative velocity approximations when applied to models of incompressible flows. The convergence rate of the scheme can only be proved to be of suboptimal 𝒪(h) order, though, based on the property of strict conservation, the robust capacity of the pair for incompressible flows is verified theoretically and numerically.

Published online:
DOI: 10.5802/smai-jcm.85
Classification: 65N12, 65N30, 76D05
Keywords: incompressible (Navier–)Stokes equations, Brinkman equations, inf-sup condition, discrete Korn’s inequality, strictly conservative scheme, pressure-robust discretization
Huilan Zeng 1; Chen-Song Zhang 1; Shuo Zhang 1

1 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computation, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {A low-degree strictly conservative finite element method for incompressible flows on general triangulations},
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Huilan Zeng; Chen-Song Zhang; Shuo Zhang. A low-degree strictly conservative finite element method for incompressible flows on general triangulations. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 225-248. doi : 10.5802/smai-jcm.85. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.85/

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