Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem

2011/10/02 by Ortner, Christoph, Zhang, Lei
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1110.0168

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.

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