论文标题
一种能量稳定的参数有限元方法，用于在三个维度中模拟固态侵蚀问题
An Energy-Stable Parametric Finite Element Method for Simulating Solid-state Dewetting Problems in Three Dimensions
论文作者
论文摘要
我们提出了一种准确且能量稳定的参数有限元方法，用于在三维空间中求解固态易碎的尖锐接口连续模型。该模型描述了与接触线迁移的薄膜\斜线蒸气界面的运动，并由触点处正确边界条件的表面扩散方程控制。我们为问题提供了一种新的弱公式，其中界面及其接触线同时进化。通过在空间和向后的Euler中使用分段线性元素，然后将弱公式离散以获得完全离散的参数有限元近似。所得的数值方法显示出良好的且无条件的能量稳定。此外，扩展了数值方法，用于求解利姆曼尼亚公制形式中各向异性表面能的固态露水的尖锐界面模型。据报道，数值结果显示了所提出的数值方法的收敛性和效率，以及对固态易碎薄膜形态演化的各向异性影响。
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line. We present a new weak formulation for the problem, in which the interface and its contact line are evolved simultaneously. By using piecewise linear elements in space and backward Euler in time, we then discretize the weak formulation to obtain a fully discretized parametric finite element approximation. The resulting numerical method is shown to be well-posed and unconditionally energy-stable. Furthermore, the numerical method is extended for solving the sharp interface model of solid-state dewetting with anisotropic surface energies in the Riemmanian metric form. Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.
