I want to solve the problem below
\begin{equation} \begin{aligned} \eta u-\Delta u &=f, &\text{in $\Omega$}\\ \end{aligned} \end{equation}
where $\Omega=(0,1)\times (0,1)$, My boundary are like this $\frac{\partial u}{\partial n} = 0$ if $y=0$ or $1$, and $u=0$ if $x=0$ or $1$. Using ghost nodes can handle the low order discretization of the neumann boundary, but the problem that i'm facing is that I want to include the four corner points in the neumann boundary not in the dirichlet one, and this causes me problem since I cannot use the interior equation on the corners.
I hope my question was clear.