Wavelet stabilization and preconditioning for domain decomposition

The aim of this paper is to propose a stabilization technique in order to circumvent the two inf–sup conditions neededfor stability of the discretization of the three fields formulationfor domain decomposition methods (following the work of Brezzi& Marini (1993) Optimisation et Controle 89–96). Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is shown to admitan asymptotically optimal preconditioner also based on wavelets. Received 24 February, 1999. Revised 7 October, 1999. ^* aivlis@ian.pv.cnr.it; http://www.ian.pv.cnr.it/~aivlis kunoth@iam.un-bonn.de; http://www.iam.uni-bonn.de/~kunoth