I tried to show the following relations for the localized pyramid basis function $\phi_{i j}(x, y)=(1-|x| /$ $h)(1-|y| / h),|x|<h,|y|<h$, where $x$ and $y$ are measured from the site $(i, j)$. of Galerkin Method.
\begin{gathered} \int d x \int d y \phi_{i, j}(x, y)=h^2 ; \quad \int d x \int d y \nabla \phi_{i, j} \cdot \nabla \phi_{i, j}=\frac{8}{3} \\ \int d x \int d y \nabla \phi_{i+1, j} \cdot \nabla \phi_{i, j}=-\frac{1}{3} ; \int d x \int d y \nabla \phi_{i, j+1} \cdot \nabla \phi_{i, j}=-\frac{1}{3} \\ \int d x \int d y \nabla \phi_{i+1, j+1} \cdot \nabla \phi_{i, j}=-\frac{1}{3} \end{gathered}
I tried to calculate the first integral, but my result is $h^2/4$.