Degree 1 Bernstein 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:

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

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

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

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

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

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

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

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

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