an encyclopedia of finite element definitions
Degree 1 Taylor 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:
\(\displaystyle l_{0}:v\mapsto\displaystyle\int_{R}v\)
where \(R\) is the reference element.
\(\displaystyle \phi_{0} = 2\)
This DOF is associated with face 0 of the reference element.
where \(R\) is the reference element.
\(\displaystyle \phi_{0} = 2\)
This DOF is associated with face 0 of the reference element.
\(\displaystyle l_{1}:v\mapsto\frac{\partial}{\partial y}v(\tfrac{1}{3},\tfrac{1}{3})\)
\(\displaystyle \phi_{1} = y - \frac{1}{3}\)
This DOF is associated with face 0 of the reference element.
\(\displaystyle \phi_{1} = y - \frac{1}{3}\)
This DOF is associated with face 0 of the reference element.
\(\displaystyle l_{2}:v\mapsto\frac{\partial}{\partial x}v(\tfrac{1}{3},\tfrac{1}{3})\)
\(\displaystyle \phi_{2} = x - \frac{1}{3}\)
This DOF is associated with face 0 of the reference element.
\(\displaystyle \phi_{2} = x - \frac{1}{3}\)
This DOF is associated with face 0 of the reference element.