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