The role of the patch test in 2D atomistic-to-continuum coupling methods
Christoph Ortner (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether (or, absence of ) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling...