  In this paper, a comparative study between the Coco-Russo scheme (based on
finite-difference scheme) and the $\mathghost$-FEM (based on finite-element
method) is presented when solving the Poisson equation in arbitrary domains.
The comparison between the two numerical methods is carried out by presenting
analytical results from the literature \cite{cocoStissi,astuto2024nodal},
together with numerical tests in various geometries and boundary conditions.
