An error analysis of a family of cell-center finite volume schemes for Poisson’s equation on Cartesian product nonuniform meshes in two dimensions is presented. Optimal-order error estimates are derived in the discrete H¹ norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh. On quasi-uniform meshes analogous estimates are obtained in the maximum norm.
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Endre Süli (1991) studied this question.
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