Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods
Antonietti, Paola F. and Ayuso, Blanca (2007) Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods. Communications in Computational Physics . (Submitted)
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We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in Antonietti et al. [Math. Model. Numer. Anal., 41(1):21-54, 2007] and [Math. Model. Numer. Anal., submitted, 2006] to the (non-consistent) super penalty discontinuos Galerkin methods introduced by Babuska et al. [SIAM J. Numer. Anal., 10:863-875, 1973] and by Brezzi et al. [Numer. Methods Partial Differential Equations, 16(4):365-378, 2000]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments demonstrating the theoretical results.
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