A Posteriori Error Estimation and Adaptive Algorithm for the Atomistic/Continuum Coupling in 2D
This work provides a theoretical foundation and practical algorithm for adaptive mesh refinement in atomistic/continuum coupling, which is important for computational materials science.
The authors developed a rigorous a posteriori error analysis and an adaptive mesh refinement algorithm for a 2D atomistic/continuum coupling method, achieving optimal convergence rates compared to a priori estimates.
Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.