A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods

Antonietti, Paola F. and Houston, Paul and Smears, Iain (2015) A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling . ISSN 1705-5105 (Submitted)

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Abstract

In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):124--149, 2011] in the sense that the resulting bound on the condition number of the preconditioned system is not only explicit with respect to the coarse and fine mesh sizes H and h, respectively, and the fine mesh polynomial degree p, but now also explicit with respect to the polynomial degree q employed for the coarse grid solver. More precisely, we show that the resulting spectral bounds are of order p^2H/(qh) for the hp-version of the discontinuous Galerkin method.

Item Type: Article
Keywords: Schwarz preconditioners, hp–discontinuous Galerkin methods
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 29 Sep 2015 10:48
Last Modified: 14 Sep 2016 22:45
URI: http://eprints.nottingham.ac.uk/id/eprint/30303

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