English

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

Numerical Analysis 2018-07-02 v1

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 P1P^1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the optimal a priori error estimates.

Keywords

Cite

@article{arxiv.1806.11106,
  title  = {A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions},
  author = {Mingjie Liao and Ping Lin and Lei Zhang},
  journal= {arXiv preprint arXiv:1806.11106},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1702.02701

R2 v1 2026-06-23T02:45:12.903Z