\( \left( \hat{K}, X\left(\hat{K}\right), \Pi_p \right) \)
defined by the following four steps

1. Geometry: \( \hat{K}=[0,1]^2 \subset {\cal R}^2 \)
2. Selection of nodes: \( \hat{a}_1, \hat{a}_2, \hat{a}_3, \hat{a}_4, \) nodes associated with element vertices (0,0), (1,0), (1,1) i (0,1), \( \hat{a}_5, \hat{a}_6, \hat{a}_7, \hat{a}_8 \) nodes associated with element edges, and \( \hat{a}_9 \) node associated with the interior of the element.
3. Definition of element shape function \( X \left( \hat{K}\right)=span \{ \hat{\phi}_j(\xi_1,\xi_2) \in {\cal Q}^{(p_h,p_v)}\left(\hat{K}\right),j=1,...,(p_h+1)(p_v+1) \} \) where \( {\cal Q}^{(p_h,p_v)}\left(\hat{K}\right) \) are polynomials of degree \( p_h \) related to the variable \( \xi_1 \) and polynomials of degree \( p_v \) related to the variable \( \xi_2 \), defined on \( \hat{K}=[0,1]^2 \). For the shape functions associated with the edge nodes of the elements, we introduce polynomials of degree \( p_1,p_3\leq p_h; p_2,p_4 \leq p_v \). We define the vertex shape functions \( \hat{\phi}_1(\xi_1,\xi_2)=\hat{\chi}_1(\xi_1)\hat{\chi}_1(\xi_2) \), \( \hat{\phi}_2(\xi_1,\xi_2)=\hat{\chi}_2(\xi_1)\hat{\chi}_1(\xi_2) \), \( \hat{\phi}_3(\xi_1,\xi_2)=\hat{\chi}_2(\xi_1)\hat{\chi}_2(\xi_2) \), \( \hat{\phi}_4(\xi_1,\xi_2)=\hat{\chi}_1(\xi_1)\hat{\chi}_2(\xi_2) \), then we define the edge shape functions, \( \hat{\phi}_{5,j}(\xi_1,\xi_2)=\hat{\chi}_{2+j}(\xi_1)\hat{\chi}_1(\xi_2), j=1,...,p_1-1 \), \( \hat{\phi}_{6,j}(\xi_1,\xi_2)=\hat{\chi}_2(\xi_1)\hat{\chi}_{2+j}(\xi_2), j=1,...,p_2-1 \), \( \hat{\phi}_{7,j}(\xi_1,\xi_2)=\hat{\chi}_{2+j}(\xi_1)\hat{\chi}_2(\xi_2), j=1,...,p_3-1 \), \( \hat{\phi}_{8,j}(\xi_1,\xi_2)=\hat{\chi}_1(\xi_1)\hat{\chi}_{2+j}(\xi_2), j=1,...,p_4-1 \), additionally, we define the interior shape functions \( \hat{\phi}_{9,i,j}(\xi_1,\xi_2)=\hat{\chi}_{2+i}(\xi_1)\hat{\chi}_{2+j}(\xi_2), i=1,...,p_h-1;j=1,...,p_v-1 \).
4. Definition of the projection-based interpolation operator \( \Pi_p:H^1\left( \hat{K} \right) \rightarrow X\left( \hat{K}\right) \). For a given function \( u \in H^1\left(\hat{K} \right) \), its projection based interpolant \( \Pi_pu\in X\left( \hat{K}\right) \) is defined by the following conditions:

\( \Pi_p u(0,0)=u(0,0) \)
\( \Pi_p u(1,0)=u(1,0) \)
\( \Pi_p u(0,1)=u(0,1) \)
\( \Pi_p u(1,1)=u(1,1) \)
\( \| \Pi_p u -u \|_{H^1_0(\hat{K})}\rightarrow min \)
where \( \| \Pi_p u -u \|_{H^1_0(\hat{K})} = \int_{\hat{K}} \left( \left( \Pi_p u \right)' -u' \right)^2 d\xi_1d\xi_2 \) is a norm in Sobolew space \( H^1_0(\hat{K}) \).

\( \left( K, X\left(K\right), \Pi_p \right) \)
defined by the following four steps

1. Geometry: \( K \subset {\cal R}^2 \)
2. Selection of nodes: \( a_1, a_2, a_3, a_4, \) nodes related to element vertices, \( a_5, a_6, a_7, a_8 \) nodes associated with element edges, and \( a_9 \) node associated with the interior of the element.
3. Definition of element shape function \( X \left( K\right)=\{ \phi(x_1,x_2) = \hat{\phi} \cdot x_K^{-1}(x_1,x_2), \hat{\phi} \in X\left(\hat{K}\right) \} \) where \( x_K:\hat{K} \rightarrow K \) is the mapping from the reference element \( \hat{K}=[0,1]^2 \) on element \( K\subset {\cal R}^2 \) dane \( \hat{K} \ni (\xi_1,\xi_2) \rightarrow x_K\left(\xi_1,\xi_2 \right)=(x_1,x_2)\in K \)
4. Definition of the projection-based interpolation operator \( \Pi_p:H^1\left( K \right) \rightarrow X\left( K \right) \). For a given function \( u \in H^1\left(K \right) \), its projection based interpolant is \( \Pi_pu\in X\left( K\right) \) is defined by the following conditions: \( \Pi_p u(a_1)=u(a_1) \)

\( \Pi_p u(a_2)=u(a_2) \)
\( \Pi_p u(a_3)=u(a_3) \)
\( \Pi_p u(a_4)=u(a_4) \)
\( \| \Pi_p u -u \|_{H^1_0(K)}\rightarrow min \)
where \( \| \Pi_p u -u \|_{H^1_0(K)} = \int_{K} \left( \left( \Pi_p u \right)' -u' \right)^2 dx_1dx_2 \) is a norm in Sobolew space \( H^1_0(K) \).