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

作　　者：Jie Chen Zhengkang He Shuyu Sun Shimin Guo Zhangxin Chen 

机构地区：[1]School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China [2]Computational Transport Phenomena Laboratory,Division of Physical Science and Engineering,King Abdullah University of Science and Technology,Thuwal 23955-6900,Kingdom of Saudi Arabia [3]School of Mathematics and Statistics,Xi'an Jiaotong Universityy Xi'an 710049,China [4]Department of Chemical&Petroleum Engineering,Schulich School of Engineering,University of Calgary,2500 University Drive N.W.,Calgary,Alberta T2N 1N4,Canada

出　　处：《Journal of Computational Mathematics》2020年第3期452-468,共17页计算数学（英文）

基　　金：The work is supported by the National Natural Science Foundation of China(No.11401467);China Postdoctoral Science Foundation(No.2013M542334.and No.2015T81012);Natural Science Foundation of Shaanxi Province(No.2015JQ1012).The work is also supported in part by funding from King Abdullah University of Science and Technology(KAUST)through the grant BAS/1/1351-01-01.

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.

关 键 词：Phase field models Solid-state dewetting SAV Energy stability Surface diffusion Finite element method 

分 类 号：O24[理学—计算数学]