When solving Poisson's equation on the unit square $\Omega$ with homogeneous Dirichlet boundary conditions for $x=0$ and Robin-type conditions at the rest of the boundary, $$ \begin{cases} -\Delta u = 0 &\quad \text{ in }\Omega,\\ u = 0 &\quad\text{ on } \Gamma_{\text{left}},\\ \alpha(u-1) = \mathbf{n}\cdot\nabla u &\quad\text{ on } \Gamma_{\text{rest}}, \end{cases} $$ the result will will of course very much depend on the value of $\alpha$.
For $\alpha\gg 1$, the Robin conditions will essentially enforce $u\approx 1$ on $\Gamma_\text{rest}$, and act as homogeneous Neumann conditions if $\alpha\ll 1$. The behavior for intermediate values is less clear.
Here are some numerical experiments for $\alpha\in\{10^0, 10^1, 10^2, 10^3\}$.
The oscillations near the boundary stand out. Is there a physical explanation for it or any way this curious behavior could be explained from the equations?