Wavelet preconditioning for the three fields formulation: Numerical results in conforming decomposition

The aim of this paper is to implement an asymptotically optimal diagonal preconditioner for the linear system stemming from the discretization of the three fields formulation. In order to apply the preconditioner based on wavelets, by introducing multiresolution analysis (MRA) for L2(0, 2) and using MRA on the unitary interval, we construct a MRA on the skeleton arising from a certain domain decomposition. Extensive numerical tests performed on a model problem confirm the optimality of the diagonal preconditioner.