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:
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},
     pages = {345--374},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {4},
     year = {2018},
     doi = {10.5802/smai-jcm.38},
     mrnumber = {3883673},
     zbl = {1416.76109},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.38/}
}
Johnny Guzmán; L. Ridgway Scott. 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/articles/10.5802/smai-jcm.38/

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