A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods
P. F. Antonietti, P. Houston & I. Smears
Int. J. Numer. Anal. Mod., 13 (2016), pp. 513-524
Published online:
2016-07
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.
Schwarz preconditioners hp-discontinuous Galerkin methods
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