AbstractA method is presented for the solution of elliptical problems defined on general‐shape multiconnected three‐dimensional domains approximated by means of polyhedra. The boundary conditions may be of the Neumann type. The differential operator and the normal derivative are discretized by generalized finite‐difference (GFD) methods using an orthogonal non‐uniform Cartesian grid. The convergence properties are analysed and the solutions of some Poisson and biharmonic problem are pr