Multigrid and Multiscale Decompositions.
Wolfgang Dahmen, Siegfried Müller, Thomas Schlinkmann · 1997
this paper is to outline a general framework for tackling problems of the above type from a somewhat different angle motivated by recent developments in the context of multiscale decomposition techniques and wavelet analysis [CDP96]. A more detailed analysis of the case of dominated convection can be found in [DMS97]. Therefore we will spend some effort on relating these concepts to multigrid methodology. This will also allow us to relate the present setting to existing methods. The discussion will be illustrated by some preliminary numerical experiments which mainly concern the case of convection-diffusion equations. In general the flow direction fi as well as the right hand side may depend on u. However, subsequent numerical experiments will be confined at this stage to the simple linear case where, however, the convective term may vary and strongly dominate the diffusive principle part, i.e., kfik AE k"k.