an encyclopedia of finite element definitions

Degree 2 Gauss–Legendre on a interval

◀ Back to Gauss–Legendre definition page
In this example:
\(\displaystyle l_{0}:v\mapsto v(0)\)

\(\displaystyle \phi_{0} = 2 x^{2} - 3 x + 1\)

This DOF is associated with vertex 0 of the reference element.
\(\displaystyle l_{1}:v\mapsto v(1)\)

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

This DOF is associated with vertex 1 of the reference element.
\(\displaystyle l_{2}:v\mapsto v(\tfrac{1}{2})\)

\(\displaystyle \phi_{2} = 4 x \left(1 - x\right)\)

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