Journal
NUMERISCHE MATHEMATIK
Volume 95, Issue 3, Pages 527-551Publisher
SPRINGER-VERLAG
DOI: 10.1007/s002110200392
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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.
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