Name
Abstract | ||
|---|---|---|
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. For simplicity, the analysis is restricted to the case of second-neighbor interactions and is linearized about a uniformly stretched reference lattice. 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 the atomistic and continuum schemes using the stability of the quasicontinuum approximation. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/08073723X | SIAM J. Numerical Analysis |
Keywords | DocType | Volume |
. quasicontinuum,coupling error,atomistic-to-continuum interface,one-dimensional quasicontinuum approximation,energy-based quasicontinuum approximation,error analysis,optimal-order convergence rate,optimal-order error estimate,quasicontinuum approximation,atomistic to continuum.,continuum limit strain,continuum scheme,quasi-nonlocal quasicontinuum approximation,continuum limit,optimal order error analysis,convergence rate | Journal | 47 |
Issue | ISSN | Citations |
4 | SIAM. J. Numer. Anal., 47:2455-2475, 2009 | 13 |
PageRank | References | Authors |
1.61 | 9 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthew Dobson | 1 | 26 | 3.88 |
| Mitchell Luskin | 2 | 124 | 23.89 |