Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements
Provides theoretical analysis for atomistic-to-continuum coupling methods, relevant to computational materials science, but the result is incremental as it confirms limited benefit of higher-order elements.
The paper formulates a patch test consistent atomistic-to-continuum coupling scheme using higher-order finite elements and proves a sharp error estimate showing optimal convergence among energy-based schemes, but finds that higher-order discretization does not qualitatively improve convergence rates.
We formulate a patch test consistent atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method in the material bulk. We prove a sharp error estimate in the energy-norm, which demonstrates that this scheme is (quasi-)optimal amongst energy-based sharp-interface a/c schemes that employ the Cauchy--Born continuum model. Our analysis also shows that employing a higher-order continuum discretization does not yield qualitative improvements to the rate of convergence.