an encyclopedia of finite element definitions
Degree 1 enriched Galerkin on a hexahedron
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- \(R\) is the reference hexahedron. The following numbering of the subentities of the reference is used:
- Basis functions:
\(\displaystyle \phi_{0} = - x y z + x y + x z - x + y z - y - z + 1\)
\(\displaystyle \phi_{1} = x \left(y z - y - z + 1\right)\)
\(\displaystyle \phi_{2} = y \left(x z - x - z + 1\right)\)
\(\displaystyle \phi_{3} = x y \left(1 - z\right)\)
\(\displaystyle \phi_{4} = z \left(x y - x - y + 1\right)\)
\(\displaystyle \phi_{5} = x z \left(1 - y\right)\)
\(\displaystyle \phi_{6} = y z \left(1 - x\right)\)
\(\displaystyle \phi_{7} = x y z\)
\(\displaystyle \phi_{8} = 1\)