We proposed a structure-preserving stabilized parametric finite element method (SPFEM) for the evolution of closed curves under anisotropic surface diffusion with an arbitrary surface energy $\hat{\gamma}(\theta)$. By introducing a non-negative stabilizing function $k(\theta)$ depending on $\hat{\gamma}(\theta)$, we obtained a novel stabilized conservative weak formulation for the anisotropic surface diffusion. A SPFEM is presented for the discretization of this weak formulation. We construct a comprehensive framework to analyze and prove the unconditional energy stability of the SPFEM under a very mild condition on $\hat{\gamma}(\theta)$. This method can be applied to simulate solid-state dewetting of thin films with arbitrary surface energies, which are characterized by anisotropic surface diffusion and contact line migration. Extensive numerical results are reported to demonstrate the efficiency, accuracy and structure-preserving properties of the proposed SPFEM with anisotropic surface energies $\hat{\gamma}(\theta)$ arising from different applications.

翻译：我们提出了一种结构保持的稳定参数有限元方法（SPFEM），用于在任意表面能 $\hat{\gamma}(\theta)$ 下的各向异性表面扩散驱动的闭合曲线演化。通过引入一个依赖于 $\hat{\gamma}(\theta)$ 的非负稳定函数 $k(\theta)$，我们获得了针对各向异性表面扩散的一种新颖的稳定守恒弱形式，并针对该弱形式提出了SPFEM离散化方法。我们构建了一个全面的分析框架，在关于 $\hat{\gamma}(\theta)$ 的极温和条件下，证明该SPFEM具有无条件能量稳定性。该方法可应用于模拟具有任意表面能的薄膜固态去湿过程，其典型特征为各向异性表面扩散和接触线迁移。我们报告了大量数值结果，以验证所提出的SPFEM在不同应用场景中出现的各向异性表面能 $\hat{\gamma}(\theta)$ 下的效率、精度和结构保持特性。