Stability of a force-based hybrid method with planar sharp interface (Q2927843)

The authors study a force-based hybrid method which couples an atomistic model with a Cauchy-Born elasticity model with sharp transition interface, i.e., there is no buffer region or transition between the atomistic and continuum regions. The regularity estimates up to the boundary for nonlinear elliptic finite difference systems are used to prove the linearized \(H^2\)-stability and convergence of the atomistic-to-continuum hybrid method. The convergence is established for hybrid schemes with planar sharp interface for systems without defects, with general finite range atomistic potential and simple lattice structure. The results are applied to some concrete examples of the atomistic-to-continuum hybrid method: triangular lattice with harmonic interaction and triangular lattice with truncated Lennard-Jones potential.