TY - JOUR T1 - A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions AU - Liao , Mingjie AU - Lin , Ping AU - Zhang , Lei JO - Communications in Computational Physics VL - 1 SP - 198 EP - 226 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0169 UR - https://global-sci.org/intro/article_detail/cicp/13319.html KW - Atomistic models, coarse graining, atomistic-to-continuum coupling, quasicontinuum method, a posteriori error estimate. AB -

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 interactions. 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.