Five-point Laplacian ($h^{-2}{\Gamma }_5$)

On a square mesh, the dimensionless five-point Laplacian is ${\Gamma }_{5}u=u_{i+1,j}+u_{i-1,j}+u_{i,j+1}+u_{i,j-1}-4u_{i,j}$. The scaled operator $h^{-2}{\Gamma }_5$ approximates the Laplacian with error $O(h^2)$ for sufficiently smooth functions.