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 - <p style="text-align: justify;">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 P<sup>1</sup> finite elements. The numerical results of the adaptive mesh
refinement algorithm is consistent with the quasi-optimal a priori error estimates.</p>