Degree 1 serendipity 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:

\(\displaystyle l_{0}:v\mapsto v(0)\)

\(\displaystyle \phi_{0} = 1 - x\)

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

\(\displaystyle l_{1}:v\mapsto v(1)\)

\(\displaystyle \phi_{1} = x\)

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