Suppose that I am looking to solve the following:
\begin{cases}
-\Delta u = f \quad &\text{on } \Omega,\\
\nabla u \cdot \textbf{n} = 0 \quad &\text{on } \partial \Omega,
\end{cases}
with the additional assumption that \int_\Omega u=0. The following question on Math Stack Exchange suggests the following: Define f \in \mathbb{R}^N be the load vector of the original problem with the components f_j = \int_\Omega f \varphi_i \,\mathrm{d}x, let g \in \mathbb{R}^N with the components g_j = \int_\Omega \varphi_j\,\mathrm{d}x, and let A be the mass matrix . Then the mean value zero is imposed by solving the modified matrix system
\begin{pmatrix}
A & g \\
g^T & 0
\end{pmatrix}
\begin{pmatrix}
u \\ \lambda
\end{pmatrix} = \begin{pmatrix} f \\ 0 \end{pmatrix},
where \lambda\in\mathbb{R} and u\in\mathbb{R}^N are the unknowns.
Is there a way to do this in FreeFemm++? If not this way, maybe some other method?