Analysis of the Cell-Centred Finite Volume Method for the Diffusion Equation

This paper presents a rigorous theoretical analysis of the cell-centred finite volume method for Poissonʹs equation. We review the traditional Taylor series expansion technique which suggests that the cell-centred method is inconsistent on nonuniform grids, which is not confirmed by numerical experiments. We then present an analysis of the method which confirms that the solution error does indeed reduce as the cell size is reduced. This is supported by numerical calculations.