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 

作者机构：School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083P.R.China Department of MathematicsUniversity of DundeeDundeeDD14HNScotlandUnited Kingdom School of Mathematical SciencesInstitute of Natural Sciences and MOE-LSCShanghai Jiao Tong UniversityShanghai 200240P.R.China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2020年第27卷第1期

页      面：198-226页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0704[理学-天文学] 0702[理学-物理学] 

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. 

主　　题：Atomistic models coarse graining atomistic-to-continuum coupling quasicontin-uum method a posteriori error estimate 

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.