An iterative finite element technique is proposed as a numerical tool to solve Poisson's equation in coaxial system during the positive DC corona discharge. The physical - mathematical model developed by Hartmann which separates the interelectrode space in two distinct regions is adopted. The magnitude of the electric field at the ionisation-region/drift-region interface in air is now well known. It is equal to the value of the minimum ionisation field which is taken as a boundary condition or a convergence criterion of space charge at this border. The effectiveness of the proposed method has been tested through its application to the coaxial system where the electric field has been measured with the linear biased probe. The obtained results are in agreement with those obtained experimentally. The classical Kaptzov's assumption, largely used in the literature, is also discussed in this work in terms of the corona wire radius. The calculated electric field at the corona wire surface, with and without resorting to the Kaptzov's assumption, shows that, for large wire radius the assumption is valid. However, for very thin wires the disagreement with the measurements values is important.