an encyclopedia of finite element definitions

# Degree 1 Kong–Mulder–Veldhuizen on a tetrahedron

◀ Back to Kong–Mulder–Veldhuizen definition page
In this example:
• $$R$$ is the reference tetrahedron. The following numbering of the subentities of the reference is used:
• $$\mathcal{V}$$ is spanned by: $$1$$, $$x$$, $$y$$, $$z$$
• $$\mathcal{L}=\{l_0,...,l_{3}\}$$
• Functionals and basis functions:
$$\displaystyle l_{0}:v\mapsto \frac{1}{24} v(0,0,0)$$

$$\displaystyle \phi_{0} = - 24 x - 24 y - 24 z + 24$$

This DOF is associated with vertex 0 of the reference element.
$$\displaystyle l_{1}:v\mapsto \frac{1}{24} v(1,0,0)$$

$$\displaystyle \phi_{1} = 24 x$$

This DOF is associated with vertex 1 of the reference element.
$$\displaystyle l_{2}:v\mapsto \frac{1}{24} v(0,1,0)$$

$$\displaystyle \phi_{2} = 24 y$$

This DOF is associated with vertex 2 of the reference element.
$$\displaystyle l_{3}:v\mapsto \frac{1}{24} v(0,0,1)$$

$$\displaystyle \phi_{3} = 24 z$$

This DOF is associated with vertex 3 of the reference element.