A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions  

作　　者：Mingjie Liao Ping Lin Lei Zhang 

机构地区：[1]School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,P.R.China [2]Department of Mathematics,University of Dundee,Dundee,DD14HN,Scotland,United Kingdom [3]School of Mathematical Sciences,Institute of Natural Sciences and MOE-LSC,Shanghai Jiao Tong University,Shanghai 200240,P.R.China

出　　处：《Communications in Computational Physics》2020年第1期198-226,共29页计算物理通讯（英文）

基　　金：supported by National Natural Science Foundation of China grant 11861131004,11771040,91430106;supported by Natural Science Foundation of China grant 11871339,11861131004,11571314,11471214 and the One Thousand Plan of China for young scientists.

摘　　要：In this paper,we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum(a/c)coupling with finite range interactions in two dimensions.We have systematically derived a new explicitly computable stress tensor formula for finite range in-teractions.In particular,we use the geometric reconstruction based consistent atomistic/continuum(GRAC)coupling scheme,which is quasi-optimal if the continuum model is discretized by P1 finite elements.The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

关 键 词：Atomistic models coarse graining atomistic-to-continuum coupling quasicontin-uum method a posteriori error estimate 

分 类 号：TN9[电子电信—信息与通信工程]