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The paper describes a new method for calculating electric field and ion current caused by overhead DC transmission lines without using the commonly used approximation, Deutsch's assumption. Unknown space functions, i.e. potential, positive and negative ion densities, are iteratively calculated from the coupled differential equations by the finite element method (FEM). The program is generally applicable to all monopolar and bipolar cases including grounded wires and wind. Emphasis is placed on numerical stability and reduced human task in the FEM computation.