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

Antonietti, Paola F.; Houston, Paul; Smears, Iain

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.

• Journal Article Type: Article
• Deposit Date: Sep 29, 2015
• Peer Reviewed: Not Peer Reviewed
• Keywords: Schwarz preconditioners, hp–discontinuous Galerkin methods
• Public URL: https://nottingham-repository.worktribe.com/output/987682