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Degree 1 Gauss–Legendre on a interval

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In this example:
\(\displaystyle l_{0}:v\mapsto v(0)\)

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

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.