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In electroencephalography (EEG) source analysis, a dipole is widely used as the model of the current source. The dipole introduces a singularity on the right-hand side of the governing Poisson-type differential equation that has to be treated specifically when solving the equation toward the electric potential. In this paper, we give a proof for existence and uniqueness of the weak solution in the function space of zero-mean potential functions, using a subtraction approach. The method divides the total potential into a singularity and a correction potential. The singularity potential is due to a dipole in an infinite region of homogeneous conductivity. We then state convergence properties of the finite element (FE) method for the numerical solution to the correction potential. We validate our approach using tetrahedra and regular and geometry-conforming node-shifted hexahedra elements in an isotropic three-layer sphere …