M. Griebel and F. Koster.
Adaptive wavelet solvers for the unsteady incompressible Navier
In J. Malek, J. Necas, and M. Rokyta, editors, Advances in
Mathematical Fluid Mechanics, Lecture Notes of the Sixth International
School ”Mathematical Theory in Fluid Mechanics”, Paseky, Czech Republic,
September 1999. Springer Verlag, 2000.
also as Report SFB 256 No. 669, Institut für Angewandte Mathematik,
Universität Bonn, 2000.
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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