We consider a fully practical finite element approximation of the nonlinear parabolic Cahn–Hilliard system

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subject to an initial condition inline image on the conserved order parameter inline image, and mixed boundary conditions. Here, inline image is the interfacial parameter, inline image is the field strength parameter, inline image is the obstacle potential, inline image is the diffusion coefficient, and inline image denotes differentiation with respect to the second argument. Furthermore, w is the chemical potential and inline image is the electrostatic potential. The system, in the context of nanostructure patterning, has been proposed to model the manipulation of morphologies in organic solar cells with the help of an applied electric field. In the limit inline image, it reduces to a sharp interface problem that models the evolution of an unstable interface between two dielectric media in the presence of a quasistatic electric field. On introducing a finite element approximation for the above Cahn–Hilliard system, we prove existence and stability of a discrete solution. Moreover, in the case of two space dimensions, we are able to prove convergence and hence existence of a solution to the considered system of partial differential equations. We demonstrate the practicality of our finite element approximation with several numerical simulations in two and three space dimensions.