Analysis of a mesh dependent stabilization for the three fields domain decomposition method

We consider a stabilized version of the three fields domain decomposition method in the finite element framework, by a variant of the stabilization proposed in [2]. Under fairly general conditions on the meshes and on the finite element discretization considered we prove that for both the two dimensional and the three dimensional case the stabilized method retains the optimality/sub-optimality properties allowed by the interpolation in the underlying discretization spaces.