EFFICIENT LINEAR SCHEMES WITH UNCONDITIONAL ENERGY STABILITY FOR THE PHASE FIELD MODEL OF SOLID-STATE DEWETTING PROBLEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Phase field models Solid-state dewetting SAV Energy stability Surface diffusion Finite element method
• 年，卷（期）: 2020,（3）
• 页码范围: 452-468
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1812-m2018-0058

摘要

In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel "scalar auxiliary variable" (SAV) approach,a new developed efficient and accurate method for a large class of gradient flows.The schemes are based on the first order Euler method and the second order backward differential formulas (BDF2) for time discretization,and finite element methods for space discretization.The proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time steps.Various numerical experiments are presented to validate the stability and accuracy of the proposed schemes.