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Two-level Schwarz preconditioners for super penalty discontinuous Galerkin methods. (English) Zbl 1364.65235

Summary: We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in [AntoniettiAyuso07,AntoniettiAyuso06] to the (non-consistent) super penalty discontinuous Galerkin methods introduced in [BabuskaZlamal73] and [BrezziManziniMariniPietraRusso00]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments confirming the sharpness of the theoretical results.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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