an encyclopedia of finite element definitions
Degree 1 enriched vector Galerkin on a tetrahedron
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- \(R\) is the reference tetrahedron. The following numbering of the subentities of the reference is used:
- Basis functions:
\(\displaystyle \boldsymbol{\phi}_{0} = \left(\begin{array}{c}\displaystyle - x - y - z + 1\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{1} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle - x - y - z + 1\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{2} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle - x - y - z + 1\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{3} = \left(\begin{array}{c}\displaystyle x\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{4} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle x\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{5} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle x\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{6} = \left(\begin{array}{c}\displaystyle y\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{7} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle y\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{8} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle y\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{9} = \left(\begin{array}{c}\displaystyle z\\\displaystyle 0\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{10} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle z\\\displaystyle 0\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{11} = \left(\begin{array}{c}\displaystyle 0\\\displaystyle 0\\\displaystyle z\end{array}\right)\)
\(\displaystyle \boldsymbol{\phi}_{12} = \left(\begin{array}{c}\displaystyle x - \frac{1}{4}\\\displaystyle y - \frac{1}{4}\\\displaystyle z - \frac{1}{4}\end{array}\right)\)