Using divergence free wavelets for the numerical solution of the Stokes problem
Karsten Urban · RWTH Publications (RWTH Aachen) · 1996
The divergence free formulation of the Stokes problem leads to a positive definite system of reduced size for the velocity, provided that divergence free trial spaces are available. The pressure is eliminated and can efficiently be computed by a postprocessing procedure. In this paper we use divergence free wavelets to construct corresponding trial spaces for a Galerkin scheme. We describe the construction, prove error estimates for the resulting scheme and show some numerical results. KEY WORDS Stokes problem, multiscale methods, wavelets, divergence free vector fields 1 Divergence free weak formulation of the Stokes problem The Stokes Problem \\Gamma\\Deltau + grad p = f in\\Omega ; div u = 0 in\\Omega ; u = g on \\Gamma = @\\Omega ; (St) is well known as a simplified model for the flow of a viscous, incompressible fluid in some open, bounded domain\\Omega ae IR n . For the numerical treatment of (St) one often uses the mixed weak formulation which leads to a saddle point probl...