A wavelet Galerkin method for the Stokes equations

The purpose of this paper is to investigate Galerkin schemes for the Stokes equations based on a suitably adapted multiresolution analysis. In particular, it will be shown that techniques developed in connection with shift-invariant refinable spaces give rise to trial spaces of any desired degree of accuracy satisfying the Ladysenskaja-Babuska-Brezzi condition for any spatial dimension. Moreover, in the time dependent case efficient preconditioners for the Schur complements of the discrete systems of equations can be based on corresponding stable multiscale decompositions. The results are illustrated by some concrete examples of adapted wavelets and corresponding numerical experiments.