Degree 1 Lagrange on a interval

• $R$ is the reference interval. The following numbering of the subentities of the reference is used:

• $\mathcal{V}$ is spanned by: $1$, $x$
• $\mathcal{L}=\{l_0,...,l_1\}$
• Functionals and basis functions:

${\displaystyle l_0:v\mapsto v(0)}$

${\displaystyle {\varphi }_0=1-x}$

This DOF is associated with vertex 0 of the reference element.

${\displaystyle l_1:v\mapsto v(1)}$

${\displaystyle {\varphi }_1=x}$

This DOF is associated with vertex 1 of the reference element.