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# Degree 1 Lagrange on a pyramid

◀ Back to Lagrange definition page In this example:
• $$R$$ is the reference pyramid. The following numbering of the subentities of the reference is used:
• • $$\mathcal{V}$$ is spanned by: $$1$$, $$x$$, $$y$$, $$z$$, $$- \frac{x y}{z - 1}$$
• $$\mathcal{L}=\{l_0,...,l_{4}\}$$
• Functionals and basis functions:
$$\displaystyle l_{0}:v\mapsto v(0,0,0)$$

$$\displaystyle \phi_{0} = \frac{- x y + \left(z - 1\right) \left(- x - y - z + 1\right)}{z - 1}$$

This DOF is associated with vertex 0 of the reference element.
$$\displaystyle l_{1}:v\mapsto v(1,0,0)$$

$$\displaystyle \phi_{1} = \frac{x \left(y + z - 1\right)}{z - 1}$$

This DOF is associated with vertex 1 of the reference element.
$$\displaystyle l_{2}:v\mapsto v(0,1,0)$$

$$\displaystyle \phi_{2} = \frac{y \left(x + z - 1\right)}{z - 1}$$

This DOF is associated with vertex 2 of the reference element.
$$\displaystyle l_{3}:v\mapsto v(1,1,0)$$

$$\displaystyle \phi_{3} = - \frac{x y}{z - 1}$$

This DOF is associated with vertex 3 of the reference element.
$$\displaystyle l_{4}:v\mapsto v(0,0,1)$$

$$\displaystyle \phi_{4} = z$$

This DOF is associated with vertex 4 of the reference element.