Before revision: In the present work, we investigate for the first time with a cut finite element method , a parameterized fourth-order nonlinear geometrical PDE, namely the Cahn-Hilliard system.
After revision: In the present work, we investigate for the first time with a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system.