An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation

Details An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation

2009-01-29

arxiv.org/abs/0901.4745v1

SIAM. J. Numer. Anal., 47:2455-2475, 2009

Mathematics

Numerical Analysis

18 pages

Scientific paper

We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the quasi-nonlocal quasicontinuum approximation. The optimal-order error estimates for the quasi-nonlocal quasicontinuum approximation are given for all strains up to the continuum limit strain for fracture. The analysis is based on an explicit treatment of the coupling error at the atomistic to continuum interface, combined with an analysis of the error due to atomistic and continuum schemes using the stability of the quasicontinuum approximation.

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