Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem
Numerical Analysis
2011-10-04 v1
Abstract
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interactions on the 2D triangular lattice, we show that patch test consistent a/c methods can be constructed for arbitrary interface geometries. Moreover, we prove that all methods within this class are first-order consistent at the atomistic/continuum interface and second-order consistent in the interior of the continuum region.
Cite
@article{arxiv.1110.0168,
title = {Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem},
author = {Christoph Ortner and Lei Zhang},
journal= {arXiv preprint arXiv:1110.0168},
year = {2011}
}