A WAVELET GALERKIN METHOD FOR THE STOKES EQUATIONS

The purpose of this paper is to investigate Galerkin schemes for the S tokes equations based on a suitably adapted multiresolution analysis. In particular, it will be shown that techniques developed in connectio n with shift-invariant refinable spaces give rise to trial spaces of a ny desired degree of accuracy satisfying the Ladysenskaja-Babuska-Brez zi condition for any spatial dimension. Moreover, in the time dependen t case efficient preconditioners for the Schur complements of the disc rete systems of equations can be based on corresponding stable multisc ale decompositions. The results are illustrated by some concrete examp les of adapted wavelets and corresponding numerical experiments.