The present paper investigates space charge formation that occurs near the surface of a solid dielectric in a weakly conducting liquid and takes place under the action of the strong external electric field and due to constant dissociation. The cases of 1D and a more complex 2D macro scale geometries are studied numerically using Comsol Multiphysics software. In the general case, the charge accumulates in a diffuse layer and can get in the bulk in consequence of its transport along the dielectric surface; and there is also a dissociation-recombination layer of ion deficit (same as in the electrohydrodynamic conduction pumping).