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Johnny Guzmán; L. Ridgway Scott
Cubic Lagrange elements satisfying exact incompressibility
SMAI-Journal of computational mathematics, 4 (2018), p. 345-374, doi: 10.5802/smai-jcm.38
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Class. Math.: 65N30, 65N12, 76D07, 65N85

Abstract

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.

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