Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  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 = { 1},
  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}