an encyclopedia of finite element definitions
Degree 2 enriched 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:
\(\displaystyle \phi_{0} = 2 x^{2} + 4 x y + 4 x z - 3 x + 2 y^{2} + 4 y z - 3 y + 2 z^{2} - 3 z + 1\)
\(\displaystyle \phi_{1} = x \left(2 x - 1\right)\)
\(\displaystyle \phi_{2} = y \left(2 y - 1\right)\)
\(\displaystyle \phi_{3} = z \left(2 z - 1\right)\)
\(\displaystyle \phi_{4} = 4 y z\)
\(\displaystyle \phi_{5} = 4 x z\)
\(\displaystyle \phi_{6} = 4 x y\)
\(\displaystyle \phi_{7} = 4 z \left(- x - y - z + 1\right)\)
\(\displaystyle \phi_{8} = 4 y \left(- x - y - z + 1\right)\)
\(\displaystyle \phi_{9} = 4 x \left(- x - y - z + 1\right)\)
\(\displaystyle \phi_{10} = 1\)