an encyclopedia of finite element definitions

# Degree 1 enriched vector Galerkin on a triangle

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In this example:
• $$R$$ is the reference triangle. The following numbering of the subentities of the reference is used:
• Basis functions:
$$\displaystyle \boldsymbol{\phi}_{0} = \left(\begin{array}{c}\displaystyle - x - y + 1\\\displaystyle 0\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{1} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle - x - y + 1\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{2} = \left(\begin{array}{c}\displaystyle x\\\displaystyle 0\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{3} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{4} = \left(\begin{array}{c}\displaystyle y\\\displaystyle 0\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{5} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle y\end{array}\right)$$
$$\displaystyle \boldsymbol{\phi}_{6} = \left(\begin{array}{c}\displaystyle x - \frac{1}{3}\\\displaystyle y - \frac{1}{3}\end{array}\right)$$