  Recent works emphasized the interest of numerical solution of PDE's with
wavelets. In their works, A.Cohen, W.Dahmen and R.DeVore focussed on the non
linear approximation aspect of the wavelet approximation of PDE's to prove the
relevance of such methods. In order to extend these results, we focuss on the
convergence of the iterative algorithm, and we consider different possibilities
offered by the wavelet theory: the tensorial wavelets and the
derivation/integration of wavelet bases. We also investigate the use of wavelet
packets. We apply these extended results to prove in the case of the Shannon
wavelets, the convergence of the Leray projector algorithm with divergence-free
wavelets.
