A new iterative scheme coupled with finite element technique is proposed as a numerical tool to solve Poisson's equation in a positive DC wire-to-plane corona using new boundary conditions. We used the model which separates the corona in two distinct regions. The ionisation region radius and the electric field at the ionisation-region/drift-region (IRDR) interface, which corresponds to a zero net ionisation coefficient of the ambient air, are developed by Hartmann in his investigation on the generalisation of the Peek's law. The proposed model allow to take into account the ionisation region thickness and thus avoids the recourse to the first Deutsch assumption, largely used in the literature. The effectiveness of the proposed method has been tested through application to the wire-to-plane geometry where the field has been measured with the linear biased probe. The agreement between the present calculated current density and electric field profiles as compared to the measured values is satisfactory.