We consider the two-dimensional convection diffusion equation with
closed characteristics on unstructured triangular meshes
and study problems with dominant convection.
We present a detailed analysis
for a representative number of model problems. The investigation is based on
Fourier analysis in the case of a very simple model problem and on numerical
experiments for more realistic situations.
The experiments have been carried
out on the software platform UG
using grids with up to 400.000 unknowns to investigate
the asymptotic behaviour.
As a result we present a multigrid scheme for this class of problems
which is robust w.r.t. to the Peclet number as well as to
the amount of crosswind diffusion introduced by the discretization scheme.
The method is based on a robust Gauss-Seidel type smoother using an ordering strategy
and a special treatment of the cyclic dependencies.
Moreover a modification of the coarse grid correction is neccessary to improve the
discrete approximation property. The presented method is of optimal
complexity (up to a logarithmic factor).