Construction of Robust Multilevel Splittings

Christoph Pflaum
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 H1-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.