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.

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