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# Degree 1 P1-iso-P2 on a interval

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In this example:
• $$R$$ is the reference interval. The following numbering of the subentities of the reference is used:
• $$\mathcal{V}$$ is spanned by: $$\begin{cases} 1 - 2 x&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\0&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$, $$\begin{cases} 2 x&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\2 - 2 x&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$, $$\begin{cases} 0&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\2 x - 1&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$
• $$\mathcal{L}=\{l_0,...,l_{2}\}$$
• Functionals and basis functions:
$$\displaystyle l_{0}:v\mapsto v(0)$$

$$\displaystyle \phi_{0} = \begin{cases} 1 - 2 x&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\0&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$

This DOF is associated with vertex 0 of the reference element.
$$\displaystyle l_{1}:v\mapsto v(1)$$

$$\displaystyle \phi_{1} = \begin{cases} 0&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\2 x - 1&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$

This DOF is associated with vertex 1 of the reference element.
$$\displaystyle l_{2}:v\mapsto v(\tfrac{1}{2})$$

$$\displaystyle \phi_{2} = \begin{cases} 2 x&\text{in }\operatorname{Interval}(((0,), (1/2,)))\\2 - 2 x&\text{in }\operatorname{Interval}(((1/2,), (1,)))\end{cases}$$

This DOF is associated with edge 0 of the reference element.