A multiscale method that couples an atomistic with a continuum model is presented. Nano-submodelling (nSM) is an approach that enables the insertion of a nano-refined submodel (atomistic) in a global model (continuum). The applied concurrent atomistic-to-continuum coupling of the two models is based on the overlapping domain decomposition scheme called the bridging domain method or on a similar method, the Arlequin method. Different models overlap and the displacement compatibility is enforced via Lagrange multipliers. In this study, an analysis of the spurious effects that may arise in and near the coupling domain is performed. Some coupling options such as energy weighting, coupling zone geometry, and the Lagrange multiplier field interpolation are tested.