Unconditionally energy-stable high-order temporal schemes for 2D solid-state dewetting

Develop high-order (order ≥ 2) temporal parametric finite element schemes for the sharp-interface model of two-dimensional solid-state dewetting with isotropic surface energy—governed by surface diffusion and contact point migration under zero-mass flux and relaxed contact angle boundary conditions—such that the fully discrete schemes are unconditionally energy stable for long-time simulations.

Background

This paper introduces temporally high-order parametric finite element methods (predictor–corrector and BDF-based) for simulating solid-state dewetting in two dimensions using the sharp-interface formulation. The authors establish well-posedness and demonstrate long-term mesh equidistribution, with numerical evidence of high-order temporal accuracy measured by manifold distance.

While the original first-order ZJB scheme is known to be unconditionally energy stable, the new high-order schemes presented here do not come with a proof of unconditional energy stability. Achieving both high temporal order and unconditional energy stability for long-time simulations under the isotropic sharp-interface model is identified as an unresolved challenge.