Wavelet stabilization and preconditioning for domain decomposition

The aim of this paper is to propose a stabilization technique in order to c ircumvent the two inf-sup conditions needed for stability of the discretiza tion of the three fields formulation for domain decomposition methods (foll owing the work of Brezzi & Marini). Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is sh own to admit an asymptotically optimal preconditioner also based on wavelet s.