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Vector bubble enriched Lagrange

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Degrees	\(1\leqslant k\leqslant 2\) where \(k\) is the Polynomial subdegree
Polynomial subdegree	\(k\)
Polynomial superdegree	\(k+2\)
Reference elements	triangle
Polynomial set	\(\mathcal{P}_{k}^d \oplus \left(\mathcal{Z}^{(11)}_{k+2}\right)^d\) ↓ Show polynomial set definitions ↓↑ Hide polynomial set definitions ↑ \(\mathcal{P}_k=\operatorname{span}\left\{\prod_{i=1}^dx_i^{p_i}\middle\|\sum_{i=1}^dp_i\leqslant k\right\}\) \(\mathcal{Z}^{(11)}_k=\left\{p\in \mathcal{P}_{k}\middle\|p=0\text{ on the boundary}\right\}\)
DOFs	On each vertex: point evaluations in coordinate directions On each edge: point evaluations in coordinate directions On each face: point evaluations in coordinate directions
Number of DOFs	triangle: \(2(k+1)^2\) (A001105)
Mapping	identity
continuity	Function values are continuous.
Categories	Vector-valued elements

Implementations

This element is implemented in Symfem .↓ Show implementation detail ↓

Examples

triangle degree 1	(click to view basis functions)
triangle degree 2	(click to view basis functions)

DefElement stats

Element added	02 March 2021
Element last updated	27 September 2024