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Degree 1 Morley–Wang–Xu on a tetrahedron
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- \(R\) is the reference tetrahedron. The following numbering of the subentities of the reference is used:
- \(\mathcal{V}\) is spanned by: \(1\), \(x\), \(y\), \(z\)
- \(\mathcal{L}=\{l_0,...,l_{3}\}\)
- Functionals and basis functions:
\(\displaystyle l_{0}:\mathbf{v}\mapsto\displaystyle\int_{f_{0}}(\tfrac{\sqrt{3}}{3})v\)
where \(f_{0}\) is the 0th face.
\(\displaystyle \phi_{0} = 6 x + 6 y + 6 z - 4\)
This DOF is associated with face 0 of the reference element.
where \(f_{0}\) is the 0th face.
\(\displaystyle \phi_{0} = 6 x + 6 y + 6 z - 4\)
This DOF is associated with face 0 of the reference element.
\(\displaystyle l_{1}:\mathbf{v}\mapsto\displaystyle\int_{f_{1}}v\)
where \(f_{1}\) is the 1st face.
\(\displaystyle \phi_{1} = 2 - 6 x\)
This DOF is associated with face 1 of the reference element.
where \(f_{1}\) is the 1st face.
\(\displaystyle \phi_{1} = 2 - 6 x\)
This DOF is associated with face 1 of the reference element.
\(\displaystyle l_{2}:\mathbf{v}\mapsto\displaystyle\int_{f_{2}}v\)
where \(f_{2}\) is the 2nd face.
\(\displaystyle \phi_{2} = 2 - 6 y\)
This DOF is associated with face 2 of the reference element.
where \(f_{2}\) is the 2nd face.
\(\displaystyle \phi_{2} = 2 - 6 y\)
This DOF is associated with face 2 of the reference element.
\(\displaystyle l_{3}:\mathbf{v}\mapsto\displaystyle\int_{f_{3}}v\)
where \(f_{3}\) is the 3rd face.
\(\displaystyle \phi_{3} = 2 - 6 z\)
This DOF is associated with face 3 of the reference element.
where \(f_{3}\) is the 3rd face.
\(\displaystyle \phi_{3} = 2 - 6 z\)
This DOF is associated with face 3 of the reference element.