Analysis of a stabilized three-fields domain decomposition method

In this paper we prove that, for suitable choices of the bilinear form involved in the stabilization procedure, the stabilized three fields domain decomposition method proposed in the paper "Wavelet Stabilization and Preconditioning for Domain Decomposition" (by S. Bertoluzza and A. Kunoth), is stable and convergent uniformly in the number of subdomains and with respect to their sizes under quite general assumptions on the decomposition and on the discretization spaces. The same is proven to hold for the resulting discrete Steklov-Poincaré operator.