an encyclopedia of finite element definitions
Degree 2 Radau on a interval
◀ Back to Radau definition page
- \(R\) is the reference interval. The following numbering of the subentities of the reference is used:
- \(\mathcal{V}\) is spanned by: \(1\), \(x\), \(x^{2}\)
- \(\mathcal{L}=\{l_0,...,l_{2}\}\)
- Functionals and basis functions:
\(\displaystyle l_{0}:v\mapsto v(0)\)
\(\displaystyle \phi_{0} = \frac{\sqrt{6} x^{2}}{3} + 2 x^{2} - 3 x - \frac{\sqrt{6} x}{3} + 1\)
This DOF is associated with vertex 0 of the reference element.
\(\displaystyle \phi_{0} = \frac{\sqrt{6} x^{2}}{3} + 2 x^{2} - 3 x - \frac{\sqrt{6} x}{3} + 1\)
This DOF is associated with vertex 0 of the reference element.
\(\displaystyle l_{1}:v\mapsto v(1)\)
\(\displaystyle \phi_{1} = - \sqrt{6} x^{2} + 4 x^{2} - 3 x + \sqrt{6} x\)
This DOF is associated with vertex 1 of the reference element.
\(\displaystyle \phi_{1} = - \sqrt{6} x^{2} + 4 x^{2} - 3 x + \sqrt{6} x\)
This DOF is associated with vertex 1 of the reference element.
\(\displaystyle l_{2}:v\mapsto v(\tfrac{3}{5} - \tfrac{\sqrt{6}}{10})\)
\(\displaystyle \phi_{2} = - 6 x^{2} + \frac{2 \sqrt{6} x^{2}}{3} - \frac{2 \sqrt{6} x}{3} + 6 x\)
This DOF is associated with edge 0 of the reference element.
\(\displaystyle \phi_{2} = - 6 x^{2} + \frac{2 \sqrt{6} x^{2}}{3} - \frac{2 \sqrt{6} x}{3} + 6 x\)
This DOF is associated with edge 0 of the reference element.