@InCollection{ Griebel.Koster:2000, author = { M.~Griebel and F.~Koster}, title = { Adaptive wavelet solvers for the unsteady incompressible {Navier Stokes} equations}, booktitle = { Advances in Mathematical Fluid Mechanics}, editor = {J.~Malek and J.~Necas and M.~Rokyta}, publisher = {Springer Verlag}, year = {2000}, note = {also as Report SFB 256 No. 669, Institut f\"ur Angewandte Mathematik, Universit\"at Bonn, 2000}, annote = {series,CNRS}, series = {Lecture Notes of the Sixth International School ''Mathematical Theory in Fluid Mechanics'', Paseky, Czech Republic, September 1999}, ps = {http://wissrech.ins.uni-bonn.de/research/pub/koster/paseckyRev.ps.gz} , abstract = { In this paper we describe adaptive wavelet-based solvers for the Navier-Stokes equations. Our approach employs a Petrov-Galerkin scheme with tensor products of Interpolet wavelets as ansatz functions. We present the fundamental algorithms for the adaptive evaluation of differential operators and non-linear terms. Furthermore, a simple but efficient preconditioning technique for the resulting linear systems is introduced. For the Navier-Stokes equations a Chorin-type projection method with a stabilized pressure discretization is used. Numerical examples demonstrate the efficiency of our appoach} }