Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy   Model for Density Functional Theory
  We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms. 
B. Langwallner, C. Ortner and E. S\"uli
math.NA math.AP