Commun. Comput. Phys., 5 (2009), pp. 296-325.

Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II - Quantitative Studies

Kolja Brix 1, Martin Campos Pinto 2, Wolfgang Dahmen 1*, Ralf Massjung 1

1 Institut fur Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany.
2 Universite Louis Pasteur, Institut de Recherche Mathematique Avancee, CNRS UMR 7501, 67084 Strasbourg, France.

Received 28 October 2007; Accepted (in revised version) 29 April 2008
Available online 1 August 2008


This paper is concerned with preconditioners for interior penalty discontinuous Galerkin discretizations of second-order elliptic boundary value problems. We extend earlier related results in \cite{BCD} in the following sense. Several concrete realizations of splitting the nonconforming trial spaces into a conforming and (remaining) nonconforming part are identified and shown to give rise to uniformly bounded condition numbers. These asymptotic results are complemented by numerical tests that shed some light on their respective quantitative behavior.

AMS subject classifications: 65F10, 65N55, 65N30

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Key words: Interior penalty method, energy-stable splittings, admissible averaging operators, frames, multilevel Schwarz preconditioners, discontinuous Galerkin methods.

*Corresponding author.
Email: (K. Brix), (M. Campos Pinto), (W. Dahmen), (R. Massjung)

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