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# Guzmán–Neilan

 Abbreviated names BR Orders $$k=1$$ Reference elements triangle, tetrahedron DOFs On each edge: (if $$k>1$$) point evaluations in tangential directions at midpoints On each facet: point evaluations in normal directions at vertices,normal integral moments with an order $$k-1$$ Lagrange space, and (if $$k>1$$) point evaluations in normal directions at midpoints of edges On the interior of the reference element: , and point evaluations at the midpoint Number of DOFs triangle: $$11$$tetrahedron: $$\begin{cases}19&k=1\\49&k=2\end{cases}$$ Mapping contravariant Piola continuity Components normal to facets are continuous Notes This element is a modification of the Bernardi–Raugel element with the facet bubbles modified to be divergence free. Categories Vector-valued elements, H(div) conforming elements, Macro elements

## Implementations

 Symfem "Guzman-Neilan"↓ Show Symfem examples ↓

## Examples

 triangleorder 1 (click to view basis functions) tetrahedronorder 1 (click to view basis functions) tetrahedronorder 2 (click to view basis functions)

## References

• Guzmán, Johnny and Neilan, Michael. Inf-sup stable finite elements on barycentric refinements producing divergence-free approximations in arbitrary dimensions, SIAM Journal on Numerical Analysis 56, 2826–2844, 2018. [DOI: 10.1137/17M1153467] [BibTeX]

## DefElement stats

 Element added 01 August 2021 Element last updated 09 December 2022