Convergence of Multigrid Algorithms for Interior Penalty Methods

V-cycle, F-cycle and W-cycle multigrid algorithms for interior penalty methods for second order elliptic boundary value problems are studied in this paper. It is shown that these algorithms converge uniformly with respect to all grid levels if the number of smoothing steps is sufficiently large, and that the contraction numbers decrease as the number of smoothing steps increases, at a rate determined by the elliptic regularity of the problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)