Commun. Comput. Phys., 5 (2009), pp. 398-412.


Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

Paola F. Antonietti 1, Blanca Ayuso 2*

1 MOX - Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy.
2 Departamento de Matematicas, Universidad Autonoma de Madrid, Campus de Cantoblanco, Ctra. de Colmenar Viejo, 28049 Madrid, Spain.

Received 30 September 2007; Accepted (in revised version) 18 December 2007
Available online 1 August 2008

Abstract

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in \cite{AntoniettiAyuso07,AntoniettiAyuso06} to the (non-consistent) super penalty discontinuous Galerkin methods introduced in \cite{BabuskaZlamal73} and \cite{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.

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

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Schwarz preconditioners, super penalty discontinuous Galerkin methods.

*Corresponding author.
Email: paola.antonietti@polimi.it (P. F. Antonietti), blanca.ayuso@uam.es (B. Ayuso)
 

The Global Science Journal