  The Surface Cauchy-Born (SCB) method is a computational multi-scale method
for the simulation of surface-dominated crystalline materials. We present an
error analysis of the SCB method, focused on the role of surface relaxation. In
a linearized 1D model we show that the error committed by the SCB method is
O(1) in the mesh size; however, we are able to identify an alternative
"approximation parameter" - the stiffness of the interaction potential - with
respect to which the error in the mean strain is exponentially small. Our
analysis naturally suggests an improvement of the SCB model by enforcing
atomistic mesh spacing in the normal direction at the free boundary.
