Bulk electroconvection pertains to flow induced by the action of the mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. There existed a long time controversy in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge selective solid, such as a metal electrode or an ion exchange membrane, is stable with respect to bulk electroconvection and whether bulk electroconvection at a nonuniform solid of this type may develop into a fully fledged flow. Numerical results reported in this paper confirm previous conclusions of a linear stability analysis concerning the nonexistence of bulk electroconvective instability, while we suggest that bulk electroconvection at a nonuniform charge selective solid results in a fully fledge flow on the length scale of nonuniformity of the surface.