A priori and a posteriori W^1,\∞ error analysis of a QC method\n for complex lattices

2012/10/07 by Assyr Abdulle, Ping Lin, Abdulle, Assyr +3
Computer Science · Engineering · #65N30 #70C20 #74G15 #74G6 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1210.2076

openalex publication_date 2012/10/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a priori and a posteriori error estimates for a\nmultiscale numerical method for computing equilibria of multilattices under an\nexternal force. The error estimates are derived in a W^1,\∞ norm in one\nspace dimension. One of the features of our analysis is that we establish an\nequivalent way of formulating the coarse-grained problem which greatly\nsimplifies derivation of the error bounds (both, a priori and a posteriori). We\nillustrate our error estimates with numerical experiments.\n

Citations

• A Computational and Theoretical Investigation of the Accuracy of\n Quasicontinuum Methods

Related

• A Posteriori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain
• Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
• On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension
• Applicability of Quasi-Monte Carlo for lattice systems
• Convergent series for polynomial lattice models with complex actions