A priori and a posteriori $W^{1,\infty }$ error analysis of a QC method for complex lattices

Abstract

In this paper we prove a priori and a posteriori error estimates for a multiscale numerical method for computing equilibria of multilattices under an external force. The error estimates are derived in a $W^{1,\infty }$ norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both, a priori and a posteriori). We illustrate our error estimates with numerical experiments.

23 pages

References in corpus (4)

• Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
• A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
• Nonlinear Elasticity from Atomistic Mechanics
• Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals