An adaptive multigrid strategy for convection diffusion problems.

*Abstract. *
For the solution of convection-diffusion problems we present
a multilevel self-adaptive mesh-refinement algorithm to resolve locally
strong varying behavior, like boundary and interior layers. The method
is based on discontinuous Galerkin (Baumann-Oden DG) discretization.
The recursive mesh-adaptation is interwoven with the multigrid solver.
The solver is based on multigrid V-cycles with damped block-Jacobi
relaxation as a smoother. Grid transfer operators are chosen in agreement
with the Galerkin structure of the discretization, and local gridrefinement
is taken care of by the transfer of local truncation errors
between overlapping parts of the grid.
We propose an error indicator based on the comparison of the discrete
solution on the finest grid and its restriction to the next coarser grid. It
refines in regions, where this difference is too large. Several results of
numerical experiments are presented which illustrate the performance of
the method.