In this study, a new 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 order, though, based on the property of strict conservation, the robust capacity of the pair for incompressible flows is verified theoretically and numerically.
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
@article{SMAI-JCM_2022__8__225_0, author = {Huilan Zeng and Chen-Song Zhang and Shuo Zhang}, title = {A low-degree strictly conservative finite element method for incompressible flows on general triangulations}, journal = {The SMAI Journal of computational mathematics}, pages = {225--248}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {8}, year = {2022}, doi = {10.5802/smai-jcm.85}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.85/} }
TY - JOUR AU - Huilan Zeng AU - Chen-Song Zhang AU - Shuo Zhang TI - A low-degree strictly conservative finite element method for incompressible flows on general triangulations JO - The SMAI Journal of computational mathematics PY - 2022 SP - 225 EP - 248 VL - 8 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.85/ DO - 10.5802/smai-jcm.85 LA - en ID - SMAI-JCM_2022__8__225_0 ER -
%0 Journal Article %A Huilan Zeng %A Chen-Song Zhang %A Shuo Zhang %T A low-degree strictly conservative finite element method for incompressible flows on general triangulations %J The SMAI Journal of computational mathematics %D 2022 %P 225-248 %V 8 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.85/ %R 10.5802/smai-jcm.85 %G en %F SMAI-JCM_2022__8__225_0
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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