We prove optimal error estimates in energy norms and related norms for a space semidiscrete and for a fully discrete approximation of the Cahn-Hilliard-Gurtin equations with source terms. Numerical simulations in one and two space dimensions illustrate the theoretical results. We also prove convergence to equilibrium for the fully discrete scheme without source terms by the use of the Łojasiewicz inequality.
"Error estimates for a finite element discretization of the Cahn-Hilliard-Gurtin equations." Adv. Differential Equations 15 (11/12) 1161 - 1192, November/December 2010.