A Multilevel Discontinuous Galerkin Method
J. Gopalakrishnan,
G. Kanschat
Abstract
A variable V-cycle preconditioner for an interior penalty finite
element discretization for elliptic problems is presented. An analysis
under a mild regularity assumption shows that the preconditioner is
uniform. The interior penalty method is then combined with a
discontinuous Galerkin scheme to arrive at a discretization scheme for
an advection-diffusion problem, for which an error estimate is
proved. A multigrid algorithm for this method
is presented, and numerical experiments indicating its robustness
with respect to diffusion coefficient are reported.