Consider the Cahn-Hilliard equation

$$\frac{\partial c}{\partial t} = \nabla^2(f(c)-\varepsilon^2 \nabla^2 c)$$

defined on your favorite domain. I'm looking for a literature reference that formally derives the linear fourth-order term $-\varepsilon^2 \nabla^2(\nabla^2 c)$ as an error term/numerical viscosity term relative to a finite difference method, when trying to naively solve the nonlinear diffusion problem

$$\frac{\partial c}{\partial t} = \nabla^2(f(c)),$$

i.e. I expect the small parameter $\varepsilon^2$ to be related to the spatial and temporal stepsize parameters.