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.

翻译：本文对求解任意区域中泊松方程时的 Coco-Russo 格式（基于有限差分法）与 $\mathghost$-FEM（基于有限元法）进行了比较研究。通过结合文献中的分析结果 \cite{cocoStissi,astuto2024nodal} 以及在不同几何形状和边界条件下进行的数值实验，对两种数值方法进行了比较。