AN ENERGY-STABLE PARAMETRICFINITE ELEMENT METHOD FOR SIMULATING SOLID-STATE DEWETTING PROBLEMS INTHREE DIMENSIONS  

作　　者：Weizhu Bao Quan Zhao 

机构地区：[1]Department of Mathematics,National University of Singapore,Singapore,119076

出　　处：《Journal of Computational Mathematics》2023年第4期771-796,共26页计算数学（英文）

基　　金：supported by Singapore MOE grant MOE2019-T2-1-063(R-146-000-296-112);supported by the Singapore MOE grant R-146-000-285-114.

摘　　要：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/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 weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian 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.

关 键 词：Solid-state dewetting Surface diffusion Contact line migration Contact angle Parametric finite element method Anisotropic surface energy 

分 类 号：O241[理学—计算数学]