The talk will focus on the numerical approximation of the evolution of a thin viscous films on a curved geometry. Here, the concept of natural time discretization for gradient flows is revisited. This is based on an explicit balance between the energy decay and the corresponding dissipation to be invested. In case of thin films the dissipation is formulated in terms of a transport field, whereas the energy primarily depends on the film profile. The velocity field and the film height are coupled by the underlying transport equation. Hence, one is naturally led to a PDE constraint optimization problem and duality techniques from optimization are applied in the minimization algorithm. For the space discretization a discrete exterior calculus approach is investigated. The method can be generalized to the simulate thin coatings.