an encyclopedia of finite element definitions

Degree 4 bubble on a triangle

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In this example:
\(\displaystyle l_{0}:v\mapsto v(\tfrac{1}{4},\tfrac{1}{4})\)

\(\displaystyle \phi_{0} = 32 x y \left(4 x^{2} + 8 x y - 7 x + 4 y^{2} - 7 y + 3\right)\)

This DOF is associated with face 0 of the reference element.
\(\displaystyle l_{1}:v\mapsto v(\tfrac{1}{2},\tfrac{1}{4})\)

\(\displaystyle \phi_{1} = 32 x y \left(- 4 x^{2} - 4 x y + 5 x + y - 1\right)\)

This DOF is associated with face 0 of the reference element.
\(\displaystyle l_{2}:v\mapsto v(\tfrac{1}{4},\tfrac{1}{2})\)

\(\displaystyle \phi_{2} = 32 x y \left(- 4 x y + x - 4 y^{2} + 5 y - 1\right)\)

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