A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

2018/06/28 by Mingjie Liao, Ping Lin, Liao, Mingjie +3
Engineering · Materials Science · #Elasticity and Material Modeling #FOS: Mathematics #Microstructure and mechanical properties #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1806.11106

openalex publication_date 2018/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is optimal if the continuum model is discretized by P¹ finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the optimal a priori error estimates.

Citations

• Convergence of a force-based hybrid method for atomistic and continuum models in three dimension
• A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D

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