Volume 13, Issue 4
A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods

P. F. Antonietti, P. Houston & I. Smears

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 513-524

Published online: 2016-07

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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 p²H/(qh) for the hp-version of the discontinuous Galerkin method.

  • Keywords

Schwarz preconditioners hp-discontinuous Galerkin methods

  • AMS Subject Headings

65N30 65N55 65F08

  • Copyright

COPYRIGHT: © Global Science Press

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