Cubic Lagrange elements satisfying exact incompressibility

Guzmán, Johnny; Scott, L. Ridgway

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.

Classification : 65N30, 65N12, 76D07, 65N85

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