Institut für Angewandte Mathematik und Statistik

Universität Würzburg, Germany

It will be presented robust multilevel algorithms for anisotropic elliptic
equations, a special class of convection diffusion equations, and Stokes'
equation. The multilevel algorithms use semi-coarsening, line-relaxation,
prewavelets, and prewavelet like functions. It is proved that the convergence
rate of the multilevel cycle is smaller than 0.2 independent of the number of
unknowns, the size of the anisotropy, and the size of the convection term.
The convection term has to be y-direction (or x-direction). The convergence
rate is smaller than 0.2 also in case of strongly varying coefficients in
y-direction, some non H^{1}-elliptic equations and a convection term
with a changing convection direction. Furthermore, we prove that the
convergence rate of a special multigrid waveform relaxation algorithm is
smaller than 0.2 independent of the time interval and the number of unknowns.