Temporally high-order parametric finite element methods for solid-state dewetting problems with isotropic surface energy

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point migration, along with appropriate boundary conditions. By incorporating the predictor–corrector strategy and the backward differentiation formula for time discretization into the energy-stable parametric finite element method developed by Zhao et al. (2021), we successfully construct temporally high-order schemes. The resulting numerical scheme is semi-implicit, requiring the solution of a linear system at each time step. The well-posedness of the fully discretized system is established. Moreover, the method maintains the long-term mesh equidistribution property. Extensive numerical experiments demonstrate that our methods achieve the desired temporal accuracy, measured by the manifold distance, while maintaining good mesh quality throughout the evolution.