Efficient design of residual-based stabilization techniques for the three fields domain decomposition method

We consider a class of residual-based stabilization schemes (including the one using wavelets) for the three fields formulation of domain decomposition of elliptic boundary value problems. These schemes can be incorporated in the plain three fields formulation as an a posteriori correction that is performed at each iteration of the numerical resolution process. The crucial point is that this approach does not require any modification to the sub-domain solvers. This fact makes it possible to design an efficient numerical algorithm that solves the discrete problem resulting from the stabilized method. We demonstrate the effectiveness of this approach by several numerical experiments that also show the low computational complexity of the stabilized method and its good dependence on the stabilization parameter.