Analysis of a Predictor-Corrector Method for Computationally Efficient   Modeling of Surface Effects in 1D
  The regular Cauchy--Born method is a useful and efficient tool for analyzing bulk properties of materials in the absence of defects. However, the method normally fails to capture surface effects, which are essential to determining material properties at small length scales. In this paper, we present a corrector method that improves upon the prediction for material behavior from the Cauchy--Born method over a small boundary layer at the surface of a 1D material by capturing the missed surface effects. We justify the separation of the problem into a bulk response and a localized surface correction by establishing an error estimate, which vanishes in the long wavelength limit. 
Andrew J. Binder, Mitchell Luskin, Christoph Ortner
math.NA