TY - JOUR
T1 - Ghost Force Influence of a Quasicontinuum Method in Two Dimension
AU - Jingrun Chen & Pingbing Ming
JO - Journal of Computational Mathematics
VL - 6
SP - 657
EP - 683
PY - 2012
DA - 2012/12
SN - 30
DO - http://doi.org/10.4208/jcm.1208-m4191
UR - https://global-sci.org/intro/article_detail/jcm/8458.html
KW - Quasicontinuum method, Ghost force, Interfacial layer.
AB - <p style="text-align: justify;">The error caused by the ghost force is studied for a quasicontinuum method with planar interface in two dimension. For a special case, we derive an analytical expression of the error, which is exploited to prove that the ghost force may lead to a finite size error for the gradient of the solution. The pointwise estimate of the error shows that the error decays algebraically away from the interface, which is much slower than that of the one-dimensional problem, for which the error decays exponentially away from the interface.</p>