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: 10.5802/smai-jcm.38
Classification: 65N30, 65N12, 76D07, 65N85

Johnny Guzmán 1; L. Ridgway Scott 2

1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Departments of Computer Science and Mathematics, Committee on Computational and Applied Mathematics, University of Chicago, Chicago IL 60637, USA
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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