@Article{IJNAM-13-513,
author = {},
title = {A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for $hp$-Version Discontinuous Galerkin Methods},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {4},
pages = {513--524},
abstract = {<p style="text-align: justify;">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 $p^{2}H/(qh)$ for the $hp$-version of the discontinuous Galerkin
method.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/450.html}
}