A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions
Provides a practical error control tool for multiscale simulations in materials science, though incremental as it extends existing GRAC coupling with adaptive refinement.
Developed residual-based a posteriori error estimates and an adaptive mesh refinement algorithm for atomistic/continuum coupling with finite range interactions in two dimensions, achieving numerical results consistent with optimal a priori error estimates.
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 $P^1$ finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the optimal a priori error estimates.