Degree 1 Crouzeix–Raviart on a triangle

• \(R\) is the reference triangle. The following numbering of the subentities of the reference is used:

• \(\mathcal{V}\) is spanned by: \(1\), \(x\), \(y\)
• \(\mathcal{L}=\{l_0,...,l_{2}\}\)
• Functionals and basis functions:

\(\displaystyle l_{0}:v\mapsto v(\tfrac{1}{2},\tfrac{1}{2})\)

\(\displaystyle \phi_{0} = 2 x + 2 y - 1\)

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

\(\displaystyle l_{1}:v\mapsto v(0,\tfrac{1}{2})\)

\(\displaystyle \phi_{1} = 1 - 2 x\)

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

\(\displaystyle l_{2}:v\mapsto v(\tfrac{1}{2},0)\)

\(\displaystyle \phi_{2} = 1 - 2 y\)

This DOF is associated with edge 2 of the reference element.