Cubic Lagrange elements satisfying exact incompressibility
The SMAI journal of computational mathematics, Tome 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.

Publié le :
DOI : https://doi.org/10.5802/smai-jcm.38
Classification : 65N30,  65N12,  76D07,  65N85
@article{SMAI-JCM_2018__4__345_0,
author = {Guzm\'an, Johnny and Scott, L. Ridgway},
title = {Cubic {Lagrange} elements satisfying exact incompressibility},
journal = {The SMAI journal of computational mathematics},
pages = {345--374},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
doi = {10.5802/smai-jcm.38},
zbl = {1416.76109},
mrnumber = {3883673},
language = {en},
url = {http://www.numdam.org/articles/10.5802/smai-jcm.38/}
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Guzmán, Johnny; Scott, L. Ridgway. Cubic Lagrange elements satisfying exact incompressibility. The SMAI journal of computational mathematics, Tome 4 (2018), pp. 345-374. doi : 10.5802/smai-jcm.38. http://www.numdam.org/articles/10.5802/smai-jcm.38/

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