Cubic Lagrange elements satisfying exact incompressibility
The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 345-374.

We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of ${C}^{1}$ piecewise quartics on the same mesh.

Published online: 2018-11-19
DOI: https://doi.org/10.5802/smai-jcm.38
Classification: 65N30,  65N12,  76D07,  65N85
@article{SMAI-JCM_2018__4__345_0,
author = {Johnny Guzm\'an and L. Ridgway Scott},
title = {Cubic Lagrange elements satisfying exact incompressibility},
journal = {The SMAI journal of computational mathematics},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
pages = {345-374},
doi = {10.5802/smai-jcm.38},
language = {en},
url={smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__345_0/}
}
Guzmán, Johnny; Scott, L. Ridgway. Cubic Lagrange elements satisfying exact incompressibility. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 345-374. doi : 10.5802/smai-jcm.38. https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__345_0/

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