We consider in $\mathbb{R}^2$ the set of points $$\{M_1(-1,1),M_2(0,1), M_3(2,1),M_4(-1,0),M_5(1,0),M_6(2,0)\}$$
Let $\Omega$ a rectangular structure consisting of the heads $\{M_4(-1,0),M_6(2,0), M_3(2,1),M_1(-1,1)\}$
Let the two polygones $\sum_1 = \{M_4,M_5,M_2,M_1\}$ et $\sum_2 = \{M_5,M_6,M_3,M_2\}$
let the mesh $\{(e_1,\sum_1,Q_1),(e_2,\sum_2,Q_2)\}$ such $$Q_1=\{f : \mathbb{R}^2 \rightarrow \mathbb{R} , f(x,y) = a + bx + cy + d xy , a , b, c , d \in \mathbb{R}\}$$
1- Proove that $(e_1,\sum_1,Q_1)$ and $(e_2,\sum_2,Q_1)$ are two finite elements of Lagrange.
2- Let $V$ the finite-dimensional space that corresponds to the mesh. Proove that $V \nsubseteqq H^1(\Omega)$
Where i can found the definition of V? (book, or paper...?) please and my second question is: dimension of $\partial \sum_1 \cap \partial \sum_2$ is 1 or 2?
