Laplacian appliaction
A first simple problem is the Laplacian problem :
\[\left\{\begin{aligned}
-\Delta u &= f \quad&&\Omega \\
u&=g \quad&&\Gamma_D \\
\frac{\partial u}{\partial n} &=h \quad &&\Gamma_N \\
\frac{\partial u}{\partial n}+u &=l \quad &&\Gamma_R \\
\end{aligned}\right.\]