The Arlequin method [1], [2] is a general numerical modeling methodology that superposes models and glues them to each others while partitioning the enrgies. Thus, by construction, this approach allows for local multimodel and multiscale analyses of existant global coarse numerical models. This multiscale methodology will be explained, analyzed [3], [4] and exemplified (e.g. [5]). As a matter of fact, the Arlequin method which is actually a local multimodel partitioning framework leads to discrete problems that are rather similar to the ones obtained when using Domain Decomposition Methods to solve monomodel problems derived from PDE's. Thus one can take advantage of the development made in the latter field to solve the discrete Lagrangian or augmented lagrangian Arlequin problems as done in [6].